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Stress Analysis and Fabrication of Composite

Monocoque Bicycle Frames

By:

Patrick L. Lizotte

Department of Mechanical Engineering

McGill University, Montréal

A Thesis Subrnitted to the Faculty of Graduate Studies and

Research in Partial Fulfillment of the Requirements of the

Degree of Master of Engineering

© Patrick Lizotte 1996

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ISBN 0-612-19874-X

Canada

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To my parents, Lise and Georges...

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Abstract

An analytical anù cxperimcntal in\"cstigation \Vas conùucteù to stlldy the ùesign anù

fabrication of carbon liber tr..lck bicycle frames. A linite clement Sofl\v;lre \Vas lIseù for the

geomctry de\"clopment. lan1inate conlïgur..ltion. and for predicting failure using the

maximum stress criteria. A load case and bounùary conditions simulating actual riding

conditions were de\"doped. The stresses in each of the composite layers \Vere found to be

lower than the allowable stresses because of a properly designed geometry and laminate.

Two composite fr..lmes were fabricated using the hand lay-up technique. using

unidirectional and wo\"en carbon fiber pre-preg material o\"er an internai foam core. Using

static testing techniques and comparisons with tr..lditional tubular frames. the carbon lïber

prototypes were shown to be betler in ail rigidity aspects. Combining the experimental and

theoretical results. a good understanding of the critical problems related to composite

monocoque bicycle fr..lffie design was obtained.

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Résumé

L·n..: ':tud..: analytiqu..:..:t ..:xpàii.i.ntal<.: a ':t': Lit..: p"ur ':tudi..:r la <:lln<:..:ptilln ..:t la fahri<:atiLln

J..: y':llls d..: pist..: faits d..: lihr..: J..: <:arhlln..: "Lln,us ..:t fahriqu':s au t..:nn..: d..: <:<.:H": r..:<:h..:r<:h..:.

l'n logi<:id d·d':m..:nts lini,. a ':1': utilis': pLlur 1<.: J,,:\·dllpp<:l1l..:nt d..: la g':Llm':tri..:. du lamin':

..:t pour pr':Jire: 1;1 rupture: ..:n utilisant 1<.: <:ritèr..: J..: <:Llntr.lint..: maximak. L"n sy,tèm..:

J'<.:fforts..:t d'..:nc:l.slr..:m..:nts simulant d..:s conditions d'utilisation a ':t': d':Ydopp.: et uti!i,':.

Les contraintes dans chacuns des pli, sont ainsi obt..:nus et sont intùieure:, aux containtes

p<:mlise, gr.1ce à une g':cm':trie et un laminé hien conçu,. Les cadre:s Je compo,ite sont

f;lbriqu':s en Ulili,ant 1<.: moulage à la main du pr-:impr-:gn': Je libre: de carbone

unidire:ctionnel et tissé ,ur un moul<.: interne de mousse. Les prototypes de libre: de carbone

sont ensuite test':s de façon statique et compar-:s à des cadre:s tr.lditionnels. Les r-:sultats de

ces tests montrent que les cadre:s de carbone sont sup.:rieurs sur tous les plans de la rigidit':.

En combinant les r-:sultals exp.:rimentaux et th':oriques. on obtient une bonne connaissance

des problèmes critiques reli':s aux cadres de \"':Ios monocoques faits de composite.

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III

Acknowledgments

1wish to thank my th.:sis sup.:rvisor Prof. Larry L.:ssard for his wnstant hdp and insight

through this \"ork. AIso sp<:cial thanks to Prof. Jam.:s N.:m.:s for his availability and

guidanc<:. 1 am aIso gr..lt.:ful to th.: t.:chnicians G.:org.: D.:dik. G.:org.: T.:wtik. Gary

Savard and Louis Hu.:ppin for th<:ir g.:n.:rous and r..lpid hdp in th.: many situations which

aros.:. 1 wish to thank the .:xchange students Fabrice Galtone. Christian Bourget. Jcan­

Philipp<: Tizi and Richard Dcvall~ of the Ecole Nationale d'Ing~nieurs de Metz (ENlM) in

Fr.lllcc for their hdp in modcl devdopment using tinitc-element analysis. My gr..ltitude also

exrcnds to Philip White for his help in the construction of the 2 prototyp.:s and to Richard

Langlois of the Centre des Matériaux Composites de St-Jérome for allowing us to us.: their

faciliùes for the final composite layup and curing of the two prototyp<:s. Aiso my sinccre

thanks to the many undergr..lduate students who worked on various aspecl~ of this project

such as the curing jig construction. and the staùc jig construction. and to Jerry Chabot for

his work on the statÎC testing of metallic fr.lll1es. 1 also wish to thank Mahmood Shokrieh.

Hamid Eskandari. Louis Brunet. Gémrd Vroomen. Jean-Fmnçois Milelte. Sylvain

Riendeau. Ann-Louise Lock and all the other past and present members of the Composites

Materials Group for their conùnued help. laughter and support. 1 wouId also like to thank

ail my friends: Martin. Nicolas. Louis. Yvan. Pierre. Pierre-André. Stéphal'':. Nathalie.

Fr.lncois. Mathieu. Matthieu. Paul. Benoit. Zaz. Dave. Sébasùen. Claude. Marie-Josée.

Jocelyn. and ail the ones l forget. who during the ùme 1have spent doing this work. stood

by closely and conùnually helped me to move forward. Et merci particulièrement à toi Julie

qui a ilIunùné ma vic durant le sprint final. La.~t but certainly not least. sinccrc thanks to

my parcnl~ Lise and Georges. my sister Martine and the !"cst of my family who have

conùnually encoumged and supported me in anything 1 dived into. Thanks again to

everyone.

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Table of Contents

Abstr.lct

R~sum~

Acknowledgments

List of Symbols

List of Figures

List of Tables

Chapter 1: Iptroduction

I.l Objective

Chapter 2: Literature Review

2. J R~view of Bicycle Fmme History

2.: Review of Fmme Building Materials2.2.1 Wood ~2.2.2 Steel2.2.3 Aluminum2.2.4 Titamum2.2.5 Magnesium2.2.6 Plastics2.2.7 Composites

2.3 Review of Carbon Fiber Fmmes2.3.1 Carbon Fiber Tube and Lug Designs2.3.2 Monocoque Diarnond Shape Carbon Fiber

Fmmes2.3.3 Bearn Bikes2.3.4 True Monocoque Shapes2.3.5 Summary ofCurrent Carbon Fiber Fmmes

2.4 Review of Bicycle Fmme Stress Analysis

2.5 Review of Manufacturing Methods2.5.1 Wet Layup2.5.2 Prepreg Internai Bladder2.5.3 Resin Tmnsfer Moulding (RTM)25.4 Therrnoset Prepreg - Vacuum Bagging2.5.4 Therrnoplasùc

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66799121313

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182022

242525262728

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Chapter 3 : Traditional Frames

~"l Rationale for Modeling and Testing Tr.lditional Fr.lmes

~"2 Finite Element Analysis of Tr.lditional Fr.lmes

~"~ Experimental Description

3.-1 Experimental and Theoretieal Techniques forTraditional Fr.lmes

3.5 Finite Element and Experimental Results

Chapter 4: Composite Frame Design

4.1 Introduction

4.2 Finite Element Analysis of the Composite Frames4.2.1 Geometrv4.2.2 Material and Laminate Contigur.ltion

4.2.2.1 Laminate Contigur~tion of Prototype 14.2.2.2 Laminate Configur.ltion of Prototype 24.2.2.3 Laminate Configur.ltion of Prototype 3

4.2.3 Loading and Boundary Conditions4.2.3.1: Starting Hypothesis of Load Case

Derivaùon4.2.3.2: Problem Steps4.3.3.3: Powers Involved4.2.3.4: Calculation of pedal :oads4.2.3.5 Considering the Complete Bicycle4.2.3.6 Ca!::ulation of the Fr.trne Torsion

Forces on the Handlebars4.2.3.7 Boundary Conditions

4.2.4 Stress Analvsis Results4.2.4.1 Prototype 14.2.4.2 Prototype 24.2.4.3 Prototype 3

Chapter 5: Composite Frame Fabrication and Testing

5.1 Introduction

5.2 Rationa!e for Manufacturing Method

5.3 Fabrication of Prototype 15.3.1 Foarn5.3.2 Foarn Adhesives5.3.3 Inserts5.3.4 Curing Jig5.3.5 Foarn-Alu:ninum Adhesive5.3.6 Carbon Fiber Materia!5.3.7 Maleria! Orientation

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424445464748

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5657586266

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='.3.S Vacuum Ba~~in~5.~.t) Curing .......5.3.10 :-'lass-Prop~rti~s of Prototyp~ 15.~.11 Conclusions and Impro\'~l1l~nts for Protl)typ~ 1

5... Elbri<:aiion of Protl1typ~ 25 1 Foam5 2 Foam Adh~siws

5 ~ lns~rts

5 Foam-Aluminum Adh~si\'~

5 .5 Int~mal Shifting Cable5 6 Carbon Fiocr :'vÏat~rial5 7 Mat~rial Ori~ntaiion

5.-4.8 Vacuum Bagging5 9 Curing ---5 10 Final Ass~mbly of Prototyp~25 11 Ma." Pro~rti~s of Prototyp~ :::5A.12 lmpro\'~m~ntsand Conclusions to Prototyp~ :::

5.5 Composite Fnune Testing5.5.1. Prototype 15.5.2 Prototy~ 2

5.6 Summary

Chapter 6 : Conclusions

Chapter 7: Recommendation for Further Research

Publications Resulting from this Work

References

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SOSOSISiS485S5s585s68788SS

898991

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List of Svrnbols~

c : StrainCi : StressCi"Xl~ : Stress at 1aaN force(l) : Anaular velocitv

~ .A : AreaC : Couple at the bottom bracketC, : Aerodynamic drag coeftïcientE : Young's ModulusEo : Wheatstone bridge outputEo. loIal : Wheatstone bridge total outputE, : Suppl)' voltageF : ForceF, : Load applied by the front wheel on the frameF:! : Load applied by the rear wheel on the frameFp : Downward force on pedalsF, : Upward force on the pedalsFwiod : Wind resistancep : Air densityP : PowerPair : Power lost due to air resistancePc)'c1is! : Power input l'rom cyclistPtolo' : Total powerr : RadiusR, : Load on front wheelR:! : Load on rear wheelS : Bike + cyclist frontal areat : TimeT : Pulling force on handlebarsTI: Pulling force from the rider's right handT, : Pulling force l'rom the rider's left handW : Weight of the rider

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List of Figures

Chaptcr 2Figurc ~.l: Lc(,)narlio D~ \ïnl...-ï s Bii..'-YL'Ic.: frlllll the..' Clldex .·\jhl1ltÎclf.\ p..'

Figur~ 2.2: Th~ DraisiClll/c l' ..

Figur~ 2.:;: Th~ (}rdil/arr Bi~yd~ l' ..

Figur~ 2...: Starl~y Sa/'·I.\· Bkyd~ p. :'-

Figur~ 2.5: Bamboo Fram~ l'. 6

Figur~ 2.6: Traditional Diamond Shape Slrlll;llIr~ p. i'

Figur~ 2.7: Ba~i~ Dim~n~ion~ of Traditional Fram~' p. 1.'

Figu~ 2.1.': ;-"lat~rial ~n~iti~~ of 5 Fram~ Building "lalcrials p. 10

Figu~ 2.9: Specilïc yloduli of 5 Framc Building "lal~rials 1'.11

Figu~ 2.10: Specitïc Yidd Str~nglh of 5 Fram~ Building "lat~rial, 1'.11

Figu~ 2.11: Prie.: per Kilogram of ylat~rial of 5 Fram~ Building "Iat~rials 1'.12

Figur~ 2.12: TREK Carbon Tub<: and Aluminum Lug ~~ign 1'.16

Figu~ 2.1:;: K~~trel 500SCI Bicyd~ Fram~ without a Scat Tub<: 1'.17

Figure 2.14: Corima Bicycl~ Frame p.li'

Figu~ 2.15: ZIPP B~am Bik~ 1'.19

Figure 2.16: Pinard10 511"0rd 1'.21

Figurc 2.17: Lotu~ Sport 11 0 Fram~ 1'.22

Figu~ 2.18: Hotta Bicyd~ 1'.22

Figu~ 2.19: Internai Bladder Techniquc 1'.26

Figure 2.20: RTM Proce~~ 1'.27

Chapter 3

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Figure 3.1: Loading Cases

Figure 3.2: Static Bicvcle Frame Testing Jig... .. ... ...Figure 3.3: Load Ccli Calibration Curve

Chapter 4

Figure 4.1: Fr.une Geometrie~ of Three Composite Monocoque Prototypes

Figure 4.2: uel Regulated Dimensions

Figure 4.3: Direction of the O· Vector

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Figure 4.4: Finite-Element Mesh and Laminate Locations for Prototype 1

Figure 4.5: Finite-Element Mesh and Laminate Locations for Prototype 2

Figure 4.6: Finite-Element Mesh and Laminate Locations for Prototype 3

Figure 4.7: Chain Drive

Figure 4.8: Forees Acting on the Bicycle

Figure 4.9: Front Wheel Free Body Diagram

Figure 4.10: Rear Wheel Free Body Diagram

Figure 4.1 1: Handlebar Forces

Figure 4.12: Riding Load Case

Figure 4.13: Riding Restraint Locations

Figure 4.14: Shear Stress Contours for Prototype 1. Layer 3

Figure 4.15: X-Nonnal Stress Contours for Prototype 1. Layer 1

Figure 4.16: Y-Nonnal Stress Contours for Prototype 1. Layer 1

Figure 4. 17: Out-of-Plane Displacement Contours for Prototype 1

Figure 4.18: Prototype 2 - XY-Shear Sn-..sses at BOllom Bracket Region. Layer 3

Figure 4.19: Prototype 2 - X-Nonnal Stress. Layer 1

Figure 4.20: Prototype 2 - Y-Nonnal Stress. Layer 1

Figure 4.21: Displacement Contours for Prototype 2

Figure 4.22 : Maximum X-Stress for Prototype 3

Figure 4.23: Maximum Y-Stress for Prototype 3

Figure 4.24: Maximum XY-Shear Stress for Prototype 3

Chapter 5Figure 5.1: Prototype 1 in the Curing Jig

Figure 5.2: Aluminurn Headset

Figure 5.3: BOllom Bracket

Figure 5.4: Rear DropoulS

Figure 5.5: Vacuum Bagging of Prototype 1

Figure 5.6: Curing Cycle

Figure 5.7: Completed Prototype 1

Figure 5.8: Head Tube Cylinder

Figure 5.9: Head Tube Plate

Figure 5.10: Bollom Bracket Insert

Figure 5.11: Scat Tube Insert

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Figure 5.12: Proto. 2- Prepreg Application

Figure 5.13: Proto. 2- Release Film

Figure 5.14: Vacuum Bag Applied to the FrJ.me

Figure 5.15 : Finished Prototype 2

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• List of tables

Chapter 3

xi

Table 3.1: Finite Element and Experimental Resull~ for Metallie Fmmes

Table 3.2: Errors Between the Finite Element and Experimental Results

Table 3.3: Steel F=e Tests Results

Chapter 4

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Table 4.1: Prototype Dimensions pAl

Table 4.2: Materia! Properties for Unidirecùonal and Woven Materials Used pA3in this Study

Table 4.3: Riding Restr:l.ints p.57

Table 4.4: Maximum Failure Index for Each Layer of Prototype 1 p.58

Table 4.5: Maximum Failure Index for Each Layer of Prototype 2 p.62

Table 4.6: Bonom Bracket Displacement with and without Reinforcement p.65

Table 4.7: Maximum Failure Index for Each Layer of Prototype 3 p.66

Chapter 5

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Table 5.1: Mechanica! Properties of the Foam Used for Prototype 1

Table 5.2: Properties of the AOCHEM High-Strenght Epoxy

Table 5.3: Summary ofWeights for Prototype 1

Table 504: Components

Table 5.5: Summary ofWeights for Prototype 2

Table 5.6: FEA and Experimenta! Results for Prototype 1

Table 5.7: FEA and Experimental Results for Prototype 2

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Chapter 1

Introduction

Thc usc of advanccd compositc matcrials is bccoming incrcasingly common. Thcy arc uscd

in numcrous applications r.lllging from acrospacc producl' to sports equipmenl. The

sporting goods industry in particular has turncd to advanced composites rccently in sports

such as cycling. hockey. and golf. The cycling industry adopted composites more than 10

years ago in the construction of high performance frames. The use of advanccd composites

materials in this industry has led to changes in the materials. gcometry and construction

technique of bicycle frames. Advanced composites arc bcing used in fr..une construction

because they allow improvemenlS in weight. stiffness. strength. and aerodynamics.

Bicycles have been part of everyday lue for more than 100 years now. They constitUle a

vital means of lI".IlIsportation for sorne. a pastime for others. and a high level competition

machine for a few. International racers are continually seeking frames which perform

bctter in order to ultimately achieve higher speeds for the same amount of frame energy

input. To achieve this goal. advanced composite materials have bcen used in the making of

high tech frames for sorne years now. However. in order to design and manufacture a

frame with these materials. a thorough engineering knowledge of composite materials.

combined with a means of analyzing a structure as complex as a bicycle frame. is essential.

1.1 Objective

The fIrst main goal of the rcsearch was to understand composite frame design through fInite

element analysis. This analysis was helpful for the determination of strength and stiffness

parameters for a frame without actually building it. The stiffness rcsults were then

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compared with a data bank of cxisting tr~ditional diamond shape fr.lmes made of steel and

aluminum in ardcr to make sure that the stiffnesses (torsion. in-plane. out-of-plane) were

improved. The second main goal was the development of a manufacturing technique for

composite prototype frames. Two monocoque carbon liber frames were constructed using

this technique. After the composite frames were constructed. the)' were statically tested to

compare their respective stiffnesses with thcir finite element models.

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Chapter 2

Literature Review

2.1 Review of Bicycle Frame History

It is believed that people have been thinking about building human powered vehicles since

the fifteenth century. A sketch named Codex AtlanticlIs [1] shown in Figure 2.1 and

attributed 10 Leonardo Da Vinci shows a device resembling a bicycle with pedals. a crank

and a chain drive connected to the rear wheel. This vehicle however did not have steering.

henee would have been unstable and thus eould not have been ridden.

Figure 2.1: Leonardo Da Vind's Bicycle from the CodexAtlanticus [1]

By the beginning of the 18oo's, unsteerable two-wheelers referred to as hobby horses

appeared in England [2]. The problem with these machines is that they could not be

balanced going down a hill al high speed as they could not be steered. Thus possibly the

most important invention in bicycle frame design was made by the German Karl Von Drais

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who disco\"ercd (possibly by error) that a front steering hobby horse couId he balanccd

going down a hill at high spced. In 1817 he built the Draisienne shown in Figure 2.2 [3].ri,: 1,

Figure 2.2 The Draisienne [3]

The ensuing evolution in bicycle design was driven by the need to use the legs in an

efficient way in order to propel the rider at the highest speed possible. The lack of an

appropriate chain drive combined with the road conditions at the time (which wouId have

made a chain drive unusable even if it existed). led to the appeamnce of the Ordinary

bicycle (high wheeler) shown in Figure 2.3 [4].

Figure 2.3 : The Ordinary Bicyele [4]

The driving front wheel was made as large as cornfortable pedaling would aIlow in order to

provide the maximum distance for eaeh pedaIing revolution and hence the highest spced

possible. The size of the front wheel was dietated by the length of one's legs. A large

Ordinary couid have adriving wheel in excess of 15m in diameter. The 1870's were the

years of dominance of these high wheelers. But severe injuries to those who fell and the

impr.ICtÎcaIities that prevented women with dresses and short or unathletic people to ride

these machine combined with the appearance of suitable ehain drives led to the more

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convcntional Safery hicyclc. The Sakry hicycle was ealieJ as such hecause it was much

safer than the Ordinary. The liN S,(/i:ry hicycle was introJuceJ in 1S69 at the lirs! Paris

velocipede show hy Andre Guilment [5J. However the Jirect JesccnJants of toJay's

bicycles were built and presented in the early 1880's at Britain's Annua! Stanley Bicycle

Show by Starley. BC' 1886. these Starlcy Safery bicycles had hall bcaring direct steering.

rubber tires and a diamond geometry very close to what we know today. Figure 2... shows

the Starlcy Safery hicycle [6]. The decades that followed Icd to retinement in the materials.

design. components and construction methods up to what we know today.

Figure 2.4: Starley Safery Bicyele [6]

After the appeurJJ1ce of cars and motoreycles relying on the interna! combustion engine.

bicycle popularity as a means of transportation dccreased in sorne countries. including

Canada and the United States. But in the 1960·s. North-America experienced the carly

signs of a bicycle reVOIUliol". Sport bikes with multiple gearing were introduced into the

adult market. Cycling was then promoted as an adult activity and as a legitimate sport that

wouId toster cardiovascular hcalth. This revolution gave every indication of bcing broad­

based. deep. and diverse. Millions of people arc now riding bikes for exereise and

tmnsportation. and the market is alive with inventiveness. Large and small scale

manufacturers arc introducing new bicycle f=es. components. and systems at a mpid

mte. Cilies arc building more and more bicycle paths in order to accommodate the

increasing traffic and the sales of bicycles arc ever increasing. We arc thus in the middle of

;:. "cycling frenzy" that the wodd has never experienced before which is favol".lble to

research into bicycle design.

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2.2 Review of Frame Building Materials

Throughout thc ycars. fr.unc building matcrials hayc cyolycd l'rom what wc now think as

ycry primitivc matcrials to space agc matcrials which wcre unknown to our socicty only 30

years ago. It is this improyement in materials which allowed to the greatest extent the

evolution in bicycle fr.unc design. This section will rcYiew most of the fr.une building. ~ ~

materials which havc been used in the past. It will show the adyantages and disadyantages

of the different materials and explain the apparition and disappcar.ll1ce of sorne of thcm.

This analysis will help to r.ltionalize the use of carbon liber material for use in this project.

2.2.1 Wood

wcod was used in the very first bicycle frames produced. Von Dmis' Draisienne and most

other hobby horses in the 18oo's were made of wood [7]. Since a minimum stiffness was

required in order to prevent enormous bending and potential collapse. hcavy wood was

otien used resulting in very heavy structures. This combincd with the tremendous work

required to shape the wood made designers and builders quickly realize that this material

was not the solution. even though sorne good wood fr.uncs were successfully built.

Around the 1870·s. metal construction becarne dominant. but wood continued to be used

spomdically in the construction offrames. rirns. and mudguards even until the 1930·s. At

sorne point. bamboo was used in the construction of fr.unes [7]. Figure 2.5 shows a

bamboo frame l'rom 1870. However because of the scarcity of this wood in thc cities. and

the increasing use and understanding of steel. wood and bamboo fr.lffies have completely

disappeare,..;.d_.-----------------------,

•..-Figure. 2.5: Bamboo Frame [7]

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2.2.2 Steel

Withoul lju.:stion. th.: us.: of st.:d in th.: past c.:ntury of hicyck fram.: construction h'IS hc.:n

domin.lOl. Many dil'f.:r.:nt alloys of st.:d ranging l'rom lo\\'-carhon sl.:ds for in.:xp<:nsiv.:

fram.:s to propri.:tary st.:d alloys of chrom.:-mclyhd.:uum-mangan.:s.: for th.: b.:st

comp<:tition fram.:s hav.: b.:.:n us<:d. Curr<:ntly. in.:xp.:nsiv.: fr.lm.:s al"<: mad.: l'rom slr.light­

gaug.: tub.:s forrn.:d l'rom st.:d strips. roll<:d and \\'dd<:d along th<: s.:am and lat.:r wdd.:d to

th.: oth.:r tub.:s of th.: fr.ln1':. B<:ll.:r fr.ln1':s ar.: mad<: l'rom s<:amkss llIocs. dr.lwn thinn<:r in

th.: middk than Olt th.: .:nds (bulling) and silv.:r braz.:d into dos<: littings tap<:r.:d Olt th.: llIOC

int.:rs.:ctions. Th<: bUlling of llIOCS is now consid.:red a sci.:n.:.: and tuoc manufactur.:rs

hav<: devdop<:d doubk and triple-bulled tuocs as weil as cir.:umfer.:ntially bUll.:d tuocs

(differcntial shape bUlling) [SI in ord<:r to allow material to be present on1y where it is really

required. Fr.ln1e build<:rs appreciate ste.:rs user-friendlin<:ss. Il oftèrs so many variabks

of dianleter. wall thickn.:ss. shap<: and metallurgy that it is almost possible to tune the

riding of a st.:.:l fmme to th.: rid<:r"s d<:sire. Tubing manufacturers such as Tange.

Reynolds. and Columbus have a complete selection of tuoc sets of different cross section

and using different alloys. As in the case of other metallic materials. the rigidity and weight

of a fr.lmeset is driven by the shap<: of the tuocs while the strength is dictated by

metallurgy. heat treatment. and/or mechanical cold working. The strongest bicycle st.:.:l

availabk is the French-made EXCELL. It has a tensile strength of more than 13S0MPa.

Among the advantages of using steel includes the fact that it is ideal for custom design. as

diftèrent tubesel~ can be chosen to provide different riding char.lcteristics for each rider.

Steel also possesses tr.lditional re.luty and can in cel1ain cascs highlight beautiful

cr.lftsmanship. Aiso. steel has remained relatively inexpensive and readily available over

the years. Steel fr.ln1es do not l'ail cata.~trophically without indication and they possess the

attr.lctive propeny of having afatigue limit. Afatigue limit is detined as the stress level

below which a material will never l'ail under fatigue loading. It reveaL~ the region close to

l'allure with cr.lcks that widen slowly in order to aIIow for an early detection of possible

l'ailure. If it does break. il is very easily repaired by heating a few joints. popping out the

damaged tube and replacing it with a new one. AlI in ail steel is a very convenient frame

building material. but beeause of its high density. it is tied to the diamond shape frame

design and in this way is condernned to fr.ln1e shapes and geometries that go back to the

19th century. Figure 2.6 shows the traditional diamond shape structure and Figure 2.7 the

1------

_....

/~'I---""

'r_....

-

•

Figure 2.6: Traditional Diamond Shape Structure [9]

•--

Figure 2.7: Basic Dimensions of Traditional Frames [10]

•

•

2.2.3 Aluminum

The tirst experimentation wilh aluminum fr.lmes oceurreu in the 189(l"s [III. The carly

frames were made l'rom cast aluminum. The tubes were joineu tog..:ther with lllgs as the

wcluing of aluminum was not well known al that time. Aluminllm tubes arc now brazeu.

wclueu or auhesiYclly bonded togelher. Sinee aluminum has a modulus km'Cr than sted.

oyersize tubes may be rcquircd in arder ta proyide a rigidity compar.lblc lo a sted fr.une

[12]. Howeyer because of its lower density. eyen larger diameters and wall thieknesses do

not result in a heaYier fr.lme. As wc incrcase the diameter of the tube the rigidily incrca.ses

to the 4th power of the diameter while the weight increa.ses following the square of the

diameter. Hence it is possible to ootain a rigid and light thune with a1uminum. E;lrly.

poorly designed aluminum tr.101es helped to build a bad reputation for aluminum frames.

ln facto carly aluminum fr.101es tended to l'ail at the tube joints l'rom improper wclding or

bonding and also l'rom fatigue failures a.s aluminllm ha.s no fatigue lilllit a.s is the ca.se with

stecl and titanium. The fact that this material does not have a jiltiglle lilllit requires the

frounes to be slightly overdesigned in order to compensate for this property of the material.

Aluminum is relatively inexpensive. light and adequatcly strong. One of the major

advantages of a1uminum over steel fr.101es is that it is non-corrosive. If properly designed

and built. a1uminum fr.101es can be a.s stiff and lively as steel fr.101es and are now among the

lightest fr.101es on the market. However. as opposed to steel thmes. these tr.lOleS are not

easily repaired and do not look !r.lditional with their often oversized tubes. As with steel.

a1uminum is relatively dense compared to composites and is thus tied to the tr.lditional

diamond shape structure. It would be pr.lctically impossible to depan l'rom the !r.lditional

diamond shape structure while still using a1uminum.

""4T' ._._. Itamum

The first use of tit::...ium in frame construction occurred in the early 1970·s. Titanium

offers bicycle designers a material 62% stiffer than aluminum but 42% lighter than steel

[12]. Titanium fr.101es are anlongst the lightest fr.101es on the market at the present time.

Titanium fr.101es are usually made l'rom commercially pure titanium (0.2% oxygen added to

pure titanium) or from 3A112.5V (3% a1uminum and 2.5% vanadium) a1loy tubes. These.

tubes are usually bought from aircraft and chemical company suppliers which sell these

tubes usually as corrosion resistant plumbing for these industries [13]. Figures 2.8. 2.9•

•10

2.10 anJ 2.1 1 show th~ J~nsiti~s. spc~ili~ moJuli. anJ spc~ili~ str~ngth anJ pri~~ of:; of

th~ mosl popular fram~ building mat~rials.

Th~ high cost of tilanium (s~e Figure 2.1 1) comes from th~ Jirticulty in ~xtr;lcting Ih~

material out of the rutile ore (TiO,) as weil as the slring~nt qualily control procedures for

components destined for the aircr..l!i industr:'. Howev~r. sorne tubing manufacturers arc

now producing "recrcational gr.lde·· titanium a1loy tubes. This gr.lde has only the

applicable propcnies suflicient for use of the material in bicycles. Another factor whieh

adds to the high pricc of titanium lr.ll1les is that titanium can only be welded in an inen

atmosphere (typically argon) sinee molten titanium instantly rcacLs with oxygen [141. The

availability of the tubes still being somewhatlimited. the designs arc limited by the available

tubes.

Material

Figure 2.8: Malerial Densities of 5 Fr.ll1le Building Malerials [15]

•

8000."..--===::--------------,

7000

6000

~5000

~4000~~ 3000c

2000

1000

o

• Steel

o Titanium

• Aluminum

!1l!I Unidirectional Carbon/Epoxy

Il Magnesium

Il

12 • Steel• 0 Titanlum_10c • Alumlnum~

"3 8~ UnidlreC!IOnal Carbon. epoxy

"""0::;; lIlll ~'agneslum

g 6,:;

'"0- 4Ul

0>

~ 2

0Malerial

Figure 2.9: Speeitie Moduli of 5 Fr.lmc: Building. :'.lalc:rials [15]

90~--------------~

80.;...---------Il!

~ 70 .;...----------Il!,5 60.;...--------0>cg 50-1--- _Ul

.g 40-'1---------­,:;

~30.;..---------­Ul

~20.;...---""..."."......-:1--­Ul

10

o

• Steel

o Titanium

• A1uminum

ll1B Unidirectional CarbonJepoxy

lIlll Magnesium

•

Malerial

Figure 2.10: Specifie Yield Strcngth of 5 Fr.tme Building Malc:riais [16]

12

60• 50

40ôii!:=30'"0U

20

10

0Malerial

• Steel

o Aluminum

• Titanium

ll§1 Unidirectional CarbonlEpoxy

Il Magnesium

•

Figure 2.11 Price per Kilogram of Malerial of 5 Frame Building Materials

Since the stiffness of titanium is moderate (belWeen that of steel and aluminum). tubes of

larger diameter than steel are often used in the design of rigid frame structures. Al:hough

the structure is rigid. a nice property of titanium is that it still offers a very comfortable and

lively ride. Like steel. titanium has a defined fatigue limit and thus at stress levels below

this limit, the frame will never degrade. If they do wear out. they are not easily repaired

because welding of titanium is a difficult process. Although many describe titanium as

being corrosion resistant, this notion is somewhat tnisleading. Actually it reacts very easily

with oxygen (hence oxides, or corrodes), but the titanium oxide actually forms a tenacious

surface layer that coats the underlying material against further intrusion [14] thus it needs

no paint and always looks new. The qualities of titanium in frame construction has

prompted many riders to adopt titanium as the material ofchoice for their frames.

2.2.5 Magnesium

Magnesium is the only other metallic material likely to be considered for bicycle frame

construction. The attractive property that lures designers to use magnesium is its low

density (66% of that of aluminum). but equivalently its modulus is only 63% of alutninum.

Hence if tubular sections are chosen for a magnesium frame they will tend to be of very

large diameter. Magnesium has been used in the production of frames by KIRK Precision

Racing Bikes [17]. They designed a cast magnesium frame with the "tubes" shaped as 1­

beams for increased rigidity due to the 10w modulus of the material [18]. It is interesting to

note !hat the availability ofmagnesium is quasi-infinite as it can be extracted from sea water

at a cost which is very reasonable. One KIRK frame uses the magnesium extracted from 1

•

•

13

cubic meter of sC>! water and costs half as much to make as an a1uminum. steel. or

composite frame [17]. But as the moduh.:s and strength of magnesium is quite low. this

material will possibly never be used extensively as a fr.lmc building matcrial.

2.2.6 Plastics

Since the advent of large molding capability for plastics. there have been severa! altempls to

mold plasùc bicycle frames. The Itera plasùc bicycle from Sweden was commercializcd in

1982 [19]. A1though this injecùon-molded bicycle had high projected sales. the project

failed completely because people were not ready for a radicai .:hange in bicycle shape and

riding feel. as plasùc allowed a departure from the tradiÙonai diamond frame geometry.

The Itera bicycle did not feel like a steel frame and ils bulk:y appearance was never acceptcd

by the community. In addiùon, early unreinforced plastics had very low modulus and

hence resulted in very bulk:y structures with relaùvely high weight. As new polymers and

polymer-based composites become readily available, tradiùonal plasùcs did not stand a

chance as a frame building material for bicycle frames. They do however retain their

potenùal as matrix materials for composite structures.

2.2.7 Composites

Fiber reinforced polymeric composites are relaùvely new to the bicycle frame market.

Since many composites offer higher strength-to-weight and sùffness-to-weight raùos than

most melal1ic materials used in frame construcùon (see 2.8,2.9,2.10). it is logical that

designers have tumed to these materials in order to fabricate lighter. stronger and sùffer

frames. The anisotropic nature of composites is very beneficial for improving the weight

of frames as reinforcement can be placed a10ng the structura! load paths rather than other

regions where low loads exist. The number of possible fiber and matrix combinaùons

a1lows the choice of exactly the desired property in a certain frame region. Different fibers

may be chosen. e.g. carbon. Kevlar and boron. and these fibers may be used in

combinaùon in the same material. In this case each fiber' s specific properùes could be used

in an opùmized way in order to give the structure desired properùes. In the pasto fiber

materials used for bicycle construction have included carbon. aramid (Kevlar. Technora).

boron. glass and Spectra fibers. These fibers were incorporated with either epoxy.

polyester. or vinylester thermosetting resins. New fibers and matrix materials appear on

the market each year with new and improved properùes. The matrix material in all frame

•

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14

constructions in the past has been thennosetting (heat-eured) resin whereas no

documentation on the use of thennoplastic (heat melting) matrix material could be found in

the literature. Thennoplastic matrices allow easy molding with excellent material properties

especially related to the increase in fracture toughness in the order of 50-100 times with

respect to thennosetting matrices [20]. Thennoplastic composites have found their way

into sorne new bike handlebars. and may revolutionize the frame building market in the

years to come. Also when the priee of eeramic and Vectran fibers and mctal matrix

composites will have come down to reasonable levels. they could be used successfully for

frame building.

Because the traditional diamond shape structure was so deeply entrenched in designers' and

manufacturers' minds. the only way to introduce new advanced composite materials into

the cycling industry was to use composite tubes to replace the steel and aluminum ones.

Composite tubes can be manufactured using the filament winding process, by rolling

woven material over a mandrel to make a tube, or by using dry woven braid with a resin

infusion process such as resin transfer moulding (RTM). Finished tubes are then

assembled in the traditional diamond shape structure using lugs which are made out of

steel, aluminum, titanium, or composite materials. However. this tube and lug approach

does not use one of the advantages of composites over metals which is their fonnability.

The tube and lug design is less than optimum and has created many problems in the past

which have given composite frames a very bad reputation. Depending on the lug material

used, problems such as galvanic corrosion at the tube-Iug interface, different thermal

expansion coefficients of the dissimiIar materials and uneven distribution of stresses

creating poor load paths at the tube intersection can occur [21]. The improper joining of the

composite tubes has also led to many failures [21]. Composite material frames should

evolve as monocoque structures because of the great formability associated with the

material and aIso in order to alleviate problems related to the joining of tubes. The way to

prevent this problem is to make a monocoque structure where the riding loads are carried

by a structure without any joints. This proposition is bener than the original solution and

gives designers unIimited creativity for the shape of the frame.

The freedom of choice for frame shape will allow development of very different structures,

which after research, may reveal qualities which couid never be achieved with diamond

shape designs. Traditionally, composite frames made with carbon, Kevlar or another fiber

type have been very expensive. But material and labor costs associated with composite

frames will become lower as the fibers and resins are much more readiIy available than in

•

•

15

the past and the manufacturing aspect is beuer known and weil understood by the

manufacturers. One problem with monocoque frames is that a new mold is required for

each frame size. which represents additional cosl~ to the manufacturer. In order to be

marketable. a bicycle frame must be available in different sizes to match the needs of the

rider. Composites do not corrode under normal atmospheric conditions and also possess

very good fatigue properties. Carbon fibers in particular are fatigue resistant even at high

stress levels. The reason for using carbon fiber as a composite material stems from the fact

that carbon fiber composites offer very high modulus at a very high strength and low

weight (see Figures 2.8.2.9.2.10). il is now readily available in many different weaves as

a preimpregnated material and is relatively inexpensive compared with other fibers such as

boron and spectra forexarnple. Carbon fibers are U.V. resistanl. AIl in aIl carbonlepoxy

composites are very weil suited for this type of high performance structure.

2.3 Review of Carbon Fiber Frames

Since the early 1970·s. carbon fiber frames have been constructed and sold by different

manufacturers. This section will atlemptto review ail important carbon fiber road bikes on

the market now in order to have an idea of what the industry has striven for in composite

construction. Current carbon fiber frames are very different from each other. Carbon fiber

frames on the market can be separated into 4 different categories in order to be more easily

described. The categories include 1) diarnond shape structures with lugs, 2) monocoque

diamond shape structures, 3) Bearn type designs and 4) other monocoque structures. This

classification will help in the description of existing carbon fiber frames.

2.3.1 Carbon Fiber Tube and Lug Designs

As described earlier, the most intuitive way to introduce carbon fiber in the construction of

frames is to make carbon fiber tubes and to join them together using sorne sort of lug.

Many manufacturers still adopt this alternative. Specialized uses titanium lugs in its S

WORKS [22] while TREK uses carbon fiber lugs in its 9000 series [22], a...,d the

Mongoose Iboc Pro SX uses a1uminum inserts [22]. The Aegis carbon frame a1so uses

a1uminum lugs bonded to carbon tubes [23]. Carbonframe's Tetra pro uses a patented

technology to Iarninate carbon fiber material to prefubricated carbon tubes through the use

of high pressure matched metal dies [24]. This technique does not yield a truly monocoque

•

•

16

structure but anempts to mininùze the effect of using dissimilar materials at the tube

intersections. The tube and lug method for manufacturing a composite frame is by far the

simplest. Sorne manufacturers will produce these frames in order to allow the cycling

enthusiast to possess a carbon frame at a relatively 10w cost (possibly in the $800 range).

However. these frames still constitute the low end of carbon fiber bicycles. Figure 2.12

shows a TREK carbon tube and aluminum lug design [25].

Figure 2.12: TREK Carbon Tube and Alumi""m Lug Design [25]

2.3.2 Monocoque Diamond Shape Carbon Fiber Frames

This second categOl)' includes frames which still possess a diamond shape structure or one

very close to it but which are constructed as a monocoque structure. These anempt to take

full advantage of the benefits ofcomposite materials while still relying on a geometry dating

back to the last century. These frames thus constitute a paradox. Perhaps they are made

for traditionalist bikers who want to obtain the maximum out of the new materials while

still retaining the look of the structure helshe rode aIl hislher life. Possibly the fmt

manufacturer to use this method was Kestrel with Brent Trimble as designer [26]. Trimble

holds most of the patents conceming carbon fiber frame monocoque construction

[27,28,29,30]. Kestrel fmt deviated from the pure diamond geometry in the construction

of a monocoque frame without a scat tube [26]. This was done in order to further reduce

the weight and to offer the rider more comfort from road perturbations. The increased

stiffness of the carbon fiber rnaterial undoubtedly allowed for this special feature. Trek

also uses monocoque construction in its OU:;V carbon series both for mountain and road

bikes [22]. Figure 2.13 shows the Kestrel 500SCI frame without a seat tube [26].

•

•

17

Figure 2.13 : Kestrel 500SCI Bicycle Frame Without Seat Tube [26]

Graphite Technology Racingbik also uses a mold to manufacture its carbon fiber

monocoque road frame [31]. They use both aluminum and steel inserts in the different

locations where the frame is attachc:d to the extemal components. This frame has the

distinctive attribute of having a curved seat tube in order to allow for the seat tube angle to

be quite shallow without hitting the rear wheel.

The Huffy corporation of Dayton, Ohio also has a monocoque frame on the market. This

frame is conslrUcted with titanium inserts and has aerodynarnic tubing [32]. This frame

was priced in the $8,000-$10,000 range in 1990 depending on if a road, mountain or !rack

version was desired. This frame is almost an identical copy of the frames that Huffy built

for the American cycling team.

Another frame which possesses characteristics similar to a diarnond geometty is the Corima

road frame. The Corima frame emerged as a fast and efficient frame in July 1993 when

Chris Boardman piloted bis bicycle to a world hour record of 52.270 kilometers [33].

Although this record has been broken since this date, the Corima remains a very highly

respected composite frame. The bicycle's design, the selection of its material and the

thickness' in the different frame locations was dictated mainly by finite-element analysis

[34]. Corima claims that the use offmite-element analysis has increased the stiffness of the

frame by 30% while achieving a weight reduction of 33% [34]. The Corima frame reveals

a very aesthetic design and has incorporated features such as internai cable routing and

•

•

18

aerodynamically shaped tubes. Nevertheless il~ geometry is based roughly on the double

triangle structure which gives the design limited variables and complex tube joining regions

where stresses might be high. Figure 2.14 shows the Corima frame [33].

Figure 2.14 : Corima Bicycle Frame [33]

2.3.3 Bearn Bikes

The next category ofbicycle to be studied and categorized are the carbon tiber monocoque

structures which do not rely on the diamond shape structure and which are often referred to

as beam bikes. This geometry is again a paradox between a diamond shape structure and a

true monocoque composite frame. Bearn bikes are those which possess a down tube, chain

stays and a top tube while eliminating the seat tube and the scat stays. The ZIPP [35] and

the Lemond y2 Boomerang [36] are beam bikes. They both have a thick Y-shaped beam

running from the head tube to the bottom bracket and continuing on towards the rear

dropout. The term beam bike comes from the fact that the scat is suspended at the end of a

cantilever beam running from the head tube to the scat (which could be referred as a top

tube if the normal diamond shape terminology is used). The main difference between the

ZIPP and the Lemond design is in the way the beam is fixed to the rest of the frame. The

Lemond design has a fixed beam position while the ZIPP beam bas a pivoting point near

the head set which allows vertical movement of the scat. The desired amount of movement

can be adjusted from almost zero displacement to almost 1.5 inches of vertical seat trave!

when riding. These frames are surprisingly light in the 12 kg range. They use a minimal

•

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19

amount of material as they only incorporate fr.une parts which are necessary to keep ail the

frame component~ together. The ZIPP has an adjusTable and even exchangeable beam

which adapts to riders of size r.mging l'rom I.60m to 1.93m. The advantage of this design

is that only one size of bicycle need be made and the actual size of the fr.une is adjusted for

each rider by changing only the beam. Unfortunately. these beam designs also have

disadvantages. As the beam acts as a cantilever structure and is unsupported at the seat

end, it allows for both vertical movement of the seat and lateral sway. The vertical

movement is relatively limited since the beam is deep with respect to its width, giving it

good rigidity in the vertical direction but not in the lateral one. This lateral sway has becn

noted as a problem in the riding of these bikes [35]. However, it seerns that the main

problem with this design is the actual geometry of the fr.une. The load transfer from the

rider's weight on the seat must be transferred in shear at the joint from the head tube to the

main down tube. The head tube region may already be higWy loaded by road forces and

moments induced by the riders arrns. so it seerns unwise that the introduction of the rider's

body weightto the rest of the frame be done al that location. The stand over height (height

of the frame at the front end of the seat) being quite high. these beam bikes are often

difficult to mount, even for experienced riders. Although they have interesting

characteristics, such as their excellent aerodynamics and low weight. the beam bikes have

had mixed success since their carly inception into the market Their limited popularity oùght

he linked to their non-conventional shape and relatively high priee. They have becn used

mostiy by triatWon riders. Figure 2.15 shows an example of the ZIPP bearn bike [37].

Figure 2.15 : ZIPP Bearn Bike [37]

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20

2.3.4 True Monocoque Shapes

This last group of carbon liber fr.lmes arc among the most stale-of-the-an carbon liber

frames. They arc structures which truly depart From the tr.tditional diamond shape

structure.

The lirst f=e to be examined is Mike Burroughs Giant prototype [38]. lt includes sorne

of the basie components of the tr.tditional dian10nd geometry. but like the beam bikes \Vith

sorne parts omitted. This f=e has the sarne backbone as the beam bikes. going From the

head tube to the bottom br.lcket and then to the rear dropouts. H<>wever. instead of holding

the scat with a cantilever top tube. Burrough's decided to attach the seat to a seeuùngly

ordinary scat tube which extends to the bottom br.tcket. Hence this fr.tme docs not have

any top tube nor scat stays. This design is much more intuitively correct than the bcam

bike because the rider's weight is tr.Insferred to a bulky bottom br.lcket arca which forms

the core of the f=e. Also the load tr.Insfer is through a compression member (the scat

tube) instead of a cantilever beam as in the case of a beam bike. This prototype. which will

most likely bccome a production mode!. combines extreme rigidity with other Pr.lctical

concems such as a low stand-over height (a fcature which the beam bikes do not have),

I:ght weight and aesthetic design. It includes internai cable routing and a monoblade front

fork.

ln 1994, five-time winner of the prestigiousTour de France Miguel lndur.lin mounled the

SlVord and succesfully broke the world hour record. Even lhough the rt.'Cord has since

been broken by Tony Rouùnger.lndurain's performance on that day was exceptional. The

Spaniard was riding on a carbon fiber monocoque f=e with titanium inserts built by

Pinarello [39.40.41]. This structure is truly unique and original as it really shows the

inventiveness of the designer. An interesting fcature of this frame is the hole in the righl

side of the structure to ailow the chain to go from the front chainring to the rear derailleur.

The SlVord dictated new standards in aerodynamics bccause the frame was only 15mm

thick (srnaller than the width of a tire) at its narrowest point while the area of higher

stresses in the bonom bracket. head sct and rear dropout regions were built up to 30mm.

Relatively heavy at I.7kg. this custom frame may never be commercialized but is believed

to be both very aerodynanùc and stiff and hence a good statement of what cau be achieved

with composites in bicycle frame construction. Figure 2.16 shows the Pinarello Sword

[41].

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21

Figure 2.16: Pinarello Sword [41]

The original Lotus fr.une which was used bv Chris Boardman to win the gold medal in the- . -1992 Barcelona O1ympics has evolved. with many changes to the production Lotus Sport

110. This monocoque carbon fiber frame has a Z-shaped structure [42]. Sorne of the

original Lotus frame features. such as the monofork and the single chainstay have been

abandoned. The LotllS Sport 110 has interesting features such as internal cable routing

and the efticient rear section of the frame which is closely faired to the rear wheel. On the

other hand. the Z-shaped structure is far from being structurally efficient. There is no

direct l('ad path for the weight of the rider to the ground. This load path must twist around

the bonom br.lcket location. where other torsion loads also exist. to reach the rear vertical

reaction point at the rear dropouts. Hence. although this fr.une is very popular. it does not

seem so well-designed structurally. Figure 2.17 Shows the LotllS Sport 110 fr.une [42].

The Hotta frame is a carbon fiOer monocoque frame which uses an X-shape [42]. From a

structuml point-of-view. this X-shape structure is very efficient for distributing the applied

loads. It provides a direct path from the headset to the rear dropouts which provides an

excellent torsional stiffness. This design also incorporates efficient fairing of the rear

wheel with the frame. This frame is of very low weight at 1.29kg because it adopts a

structurally efficient design and thus requires a nùnimum amount of material. A frame of

this type alIows very easy internal cable routing along the main beam. Figure 2.18 Shows

the Hotta bicycle [43].

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22

Figure 2.17: Lotus Sport 110 Frame [42]

Figure 2.18: Hotta Bicycle [43)

2.3.5 Summary of Current Carbon Fiber Frames

This review ofcarbon fiber frames on the market is far from being complete. but it helps to

understand why current diarnond shape frames or monocoque structures are used. It also

provides a framework for comparison with the prototypes which will be developed during

this project.

•

•

2.4 Review of Bicycle Frame Stress Analysis

Stress analysis using linite·c1ement techniques is a good way to analyze a complex

composite structure. Many published studies document the use of linite-c1ement analysis in

the design of tr.lditional tubular frames [44.45.46.47]. The simplest way to perform a

linite·c1ement analysis on the tmditional diamond structure is to use beam c1emenL~ to

mode! thc tubes. The beam e!cment can accur.ltcly account for the tube pammetcrs of

thickness. oUL~ide dimneter and matcrial proper.ies. If sufficient number of clements are

utilized. double butting of tubes can also be easily incorpor.ltcd into the mode!.

Using the beam c1emcnt method and a load case where a cyclist is in a sprint out of the

pedals on a tr.lditional mctallic diamond fr.une. it was found that the ma.ximum stress was at

the intcrsection of the down tube and the seat tube at thc bottom br.lcket [48]. A study of

the same type. but considering rider induced loads al different cr.lnk angles combincd with

handlebar and seat loads. found that thc maximum stress is at the top and seat tube

intersection [44]. The beam mode! approach is approximate as it does not consider the

actual tube joining regions where large stresses and failure usually occurs and could not

mode! a composite structure consisting of many plies of material. This is why the use of

shell elemenL~ to model the tubes themselves and the joinL~ has also been considered [45].

Shell models allow the detcrnùnation of the different tube stresses around the

cireumference. something that beam models cannot provide. However. it was shown that

deflection measuremenL~ on both shell and bearn finite-element models were very sirnilar

for static loading cases [47]. Therefore. if del1ections are the main concem and not failure.

a bearn model is sufficient.

In a good design. the strengths of the different tubes must be high enough to prevent

failure. coupied with a design goal that the f=e be stiff in certain regions and compliant in

others. It is desimble to have a stiff head tube and bollom bmcket region in order to

prevent excessive deformations during cases of high loading during intense riding. On the

other hand. a vertically compliant fr.une would be desimble for riding comfort. Hence.

characterization of bicycle frames must be done in terms of strength in order to assure

structural integrity. but also must be done in terms of stiffness in order to produce a good

f=e. F=es can also be characterized by the strain energy absorbed into the frame

during pedaling. As energy is most effectively transferred through a stiff structure from the

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24

rider"s body to the baek whee!. a minimum of strain energy stored by the frame under

loading is desirable [46].

It is diffieult to eompare bicycle fmmes since each researcher and manufacturer utilizes a

different loading case or test method to chamcterize their frames. This is so because there

are very few standards for the detennination of performance of bicycle frames. The

existing standards are mostly for security and structuml integrity and cannot be used

directly to compare performance and rigidity of different fr.lmes. These standards offer

only statie and dynamic testing where one load is applied to one point whereas this is not

what happens in actual riding situations. Hence the standards are sometime only useful to

make sure that bicycles respect a certain baseline of structuml integrity but not as a design

tool for high performance r.lcing bicycles. However. new initiatives in bicycle standards

l'rom ISO [49]. JSA [50] and ASTM [51] will greatly contribute to the standardization of

test methods in the near future.

Since it is believed that high performance tmck and time trial composite bicycles should

evolve into the shape of monocoque tubeless frames. the lessons learned l'rom the tinite­

element analysis of tubular fr.lI11es may not be relevant. This rese.lfch is thus aimed at using

tinite-element methods to perform stress analysis on monocoque composite fmmes r.lther

than on conventional tubular fmmes. Another study on monocoque composite material

frames has been performed but concenlr.ltes mainly on the construction process and testing.

and no tinite-element analysis was performed [52]. Also a study of a composite mountain

bike was performed but only considers finite-element static loading at one location to be

compared with the actual prototype. and docs not review the stresses during actual riding

conditions [53]. The use of a geometrically efficient structure combined with the desimble

properties of composites. a correct understanding of the loading and boundary conditions.

as weil as stress and failure analysis are ail important facLors for the development of a good

composite bieycle frame.

2.5 Review of Manufacturing Methods

Many methods can be employed to manufacture a composite structure. For the case of a

composite monocoque bicycle frame, more than one fabrication method exists. Each

method has its advantages and disadvantages. Hence. for a certain application, it is

important to know which method to use. This section will provide a quick non-exhaustive

•

•

ovcrvit:w of thc possihle fahrication mcthoùs for thc C(>nstruction (,fa composite hieycle

framc.

2.5.1 Wct La)'up

This methoù inn)l\"cs the application of ùry fahrie wetteù with an appropriate resin 0\"Cr a

previously shapcù foam core. The libers anù resin arc purchaseù separatdy. as opposeù to

preimpregnated materiaJ where the appropriate 4uantity of re,in is aJreaùy mixeù with the

libers. In the wet layup process. each layer of materiaJ is wetted with the resin and placed

on the structure. It is then allowed to room temper.lture cure. The main advantage of

buying the libers and resin separ.ltdy is (hat it is less expensive. Aiso it allu,,"s. up to a

certain extent. the choice of any libers to be used with any resin. There arc also many

disadvantages with this method. Although it is a rdiable process. it is by nature very slow

and labour intensive. Since no pressure is used during the curing process. the plies arc not

forced together in any way. This prevents the correct consolidation of the unbonded plies

into a bonded lanlinate. For this reason. this method is otien linùted to low-tech

applications where the interply bonding is not critical. Since this method uses an internai

open mouId. it will create a surface linish that may not be pcrfecl. Extensive sanding and

làiring will be required in order to obtain the proper surface quality. Aiso in order to assure

a good bonding between layers. it is otien required to sand in bet\Veen each layer again

increasing the labor lime. But the main disadvantage \Vith this method is the fact that it

otien results in heavy pieces as the volume fr.lction of liber and resin is difticult to control.

For structur.J.I consider.llions. it is better to have a resin rich structure than a resin delicient

one where it will be easier for cr.lcks to form and propagate. For this reason. more resin

than required is often added. resuIting in a heavicr structure.

2.5.2 Prepreg with Internai Bladder

This fabrication method involves a re-usable :2 or 3-part external mould. inside \Vhich an

internai bladder is used to create pressure on the preimpregnated material against the mould.

This fabrication method thus requires a re-usable mould made of alunùnum. epoxy.

liberglass or any other mould making material. The appropriate layup il' placed on the

mould with the preimpregnated material. After the layup is linished. a nylon/polyethylene

bladder is placed on one half of the mould. The mould is then c10sed and the bladder

inflated to a proper pressure. The mould is then placed in an oven for curing to take place.

•

•

26

This method produces an excellent surface finish because the extemal layer of the structure

is forced against the finished surface of the mould. This method has successfully been

used in the producùon of bicycle fr.unes for sorne Ùme now [54]. It is appropriate for

medium to large scale production. but not for small scale prototyping. It is thus an

expensive fabricaùon method for small quanùùes. but rapidly becomes worthwhile if many

pieces are to be produced. It provides a very light structure as it is internally filled with air

instead of the internai foarn used in sorne other methods. The thin nylon/polyethylene film

remains part of the structure after the curing has taken place. This method is quick and

clean. A frame can be produced in 2-3 hours with this method compared with 2-3 days

using the wet layup technique. This method cannot be completely automated, because it

sùll requires the hand layup of the composite prepreg in the mould. The internai bladder

technique is used in the construcùon ofbikes such as the Antelope [54]. the TREK OLCV

Carbon Series [26] and many other carbon frames. Figure 2.19 shows a schemaùc of the

internai bladder technique.

MoutdMQnom~teor

Figure 2.19: Internai BladderTechnique [55]

2.5.3 Resin Transfer Moulding (RTM)

In Resin Transfer Moulding (RTM), dry reinforcement is placed inside a 2 or 3 part mould.

The mould is then closed and a catalyzed resin is injected into the mould via a centrally

located injection point. The resin injection point is located so as to provide equal wetting of

the fibers everywhere in the mould. As the resin spreads through the mould, it displaces

the entrapped air through the air vents and impregnates the fibers. Depending on the resin

system used. the curing cao be done at room temperature or in a controlled temperature

•27

oyen. Similar to the internai bladder method. this construction technique uses an external

mould which may be improper for a small production. However it provides a very good

surface finish. In order to produce a bicycle frame with this method. it might be necessary

to use an internai foam core in the mould in order to provide the required wall thickness.

But for the making of a very thin bicycle frame such as the ones often used in ùme trials.

composites with no internai core may be used. Figure 2.20 shows a schematic of the R1M

process.

c--- .

dry libers

internai foam core

resin injectio~

irli1--------\ i

=.

mold""-"""",,,,"""""-7'--:::;

tp'lL/(j

Figure 2.20: RTM Process [20]

2.5.4 Thermoset Prepreg - Vacuum Bagging

•

Like the wet layup method. the vacuum bagging method involves the fabricaùon of an

internai core over which the composite rnaterial is placed. Foam or other materials with

appropriate properùes can be used as a core. A1uminum inserts are then secured at the

appropriate locaùons on the core with glue. The frame is then ready to be covered with

composite material. The rnaterial has a tad.")' feel and thus adheres weil directly on the

foam. The layers are applied one after the other in a specified sequence. After the

composite materiallayup is done. a layer of release film and breather material is added. A

large vacuum bag is then made over the part The bagging material is very resistant to tcars

and stretching. A vacuum is then drawn from under the bag. creating pressure on the part.

This pressure has many uses such as assuring that there are no air bubbles trapped between

layers. This problem often occurs in the wet layup technique. because there is nothing

forcing the layers together during curing. so the compacùon is often very poor. The

vacuum bagged part is then placed in a controlled temperalure oyen for a specified Ùffie to

allow full curing. The second use of pressure is to allow the resin to flow before the aetuaI

curing. As the resin heats up. it flows from resin rich to resin poor areas. The vaccum

bagging-prepreg technique does not yield a perfect surface finish. The quality of the finish

•

•

28

is very much dependcn! on the quality of the vacuum bag. Often sanding is required after

the curing in order to remove resin wrinkles. A primer and pain! can then be applied so as

to improve the surface finish.

2.5.4 Thermoplastic

Instead of using a thermosetting composite. it is possible to use a thermoplastic material.

The thermoplastic matrix (PEEK. PPS. Polysulfone. Polyimide. etc.) can be used with

almost ail of the conventional fibers in order to make a prepreg. This prepreg is dry and

can he kept at room temperature. The method of using the thermoplastic prepreg is the

same as the thermoset prepregs and thus could be used in the internai bladder or vaccum

bagging method. Thermoplastic prepregs are not as weIl known as the conventionnai

thermosets as they are newer and have not been used in as many applications. They are

often used in high-tech applications were fracture toughness is important. This property is

very important for bicycle frames. hence they could be used in the near future. The

problem with thermoplastics is that they are not tacky at room temperature and hence it may

he difficult to construct a layup of many superimposed layers on an intricate shape.

•

•

29

Chapter 3

Traditional Frames

3.1 Rationale for Modeling and Testing Traditional Frames

Although this research concentrates on composite frames. it is important to understand how

and why traditional frames should be improved upon. Thus. as part of this research, a

summary investigation of traditional metallic bicycle frames was performed. Some

traditional frames were modeled using finite element analysis (FEA) and then tested using a

specially built testing jig in order to quantify their stiffness in different directions and to

correlate results with the FEA models. The results also provide baseline values for frame

stiffness. so that valid conclusions can be made for the new composite structures. This

preliminary static testing of traditional frames also permiued to establish the experimental

procedure required for the static testing of the composite frames.

3.2 Finite Element Analysis of Traditional Frames

The finite element analysis of traditional frames was performed in order to quantify the

stiffness of these frames, and also to show that correlation between the finite element

results and the testing jig could be obtained. The finite element analysis was performed

using SRDC'S l-OEAS software [56] at McGill University. This fmite element software

combines good 3-0 graphies, element library and pre- and post-processing.

In order to model traditional bicycle frames, two approaches were utilized. The fIrSI one

considered each tube of the frame as a beam element, thus creating a beam frame structure.

The inside and outside diameters of the beams were cross-section material properties of the

beam elements. Thus the beam elements could be defined by thcir end-point locations in 3-

•

•

30

D space. This procedure is simple but. as will be seen later. does not yield ail the

necessary results. A typical fr.une modeled using this technique may contain only 10

elemenL~ and be readily solved requiring minimal computer time. The other approach is to

model the whole frame using ~hell clements. This procedure models each tube with

rectangular and triangular thm s;.1ell elements. The tubes may contain 6-8 such elements

around their circumferences. and an appropriate amount along their length resulting in

models with over 1000 shell elements and thus requiring more extensive computer lime.

The geometry of the junction between the tubes is achieved manually by creating triangular

or rectangular thin shen elements connecting thc intersecting tubes. It is obviously much

simpler to model a frame using beam elements but a better analysis is donc by

understanding the tube intersection stress analysis. Depending on the results required

(stiffness or strength) an appropriate choice of modeling techniquc can be chosen. The

modeling of a frame using beam elements can yield fairly accurate displacements and thus

stiffness parameters. However. it is difficult to obtain an accurate account of the stress

levels and patterns associated with the structure. On the other hand. if wc use thin shen

elements. in addition to accurate displacement results. the longitudinal and circumfcrential

stresses present in the tubes can also be obtained. Hence if a stiffness-only study is

required. beam elements modeling the frame might be sufficient for certain stiffness

measurements. On the other hand. if a complete stiffness and strength study is required.

thin shen finite elements should be used to model a traditional tubular frame.

3.3 Experimental description

In order to effectively compare different frames. a series of static tests were developed.

Each test corresponds to a different loading case where forces are applied to different parts

of the frames and where other parts of the frames are restrained. The different static tests

are shown in Figure 3.1.

The individual tests are aimed at measuring a different char.lcteristic that may or may not be

beneficial to the rider and thus characterizes a good or a bad frame. A description of each

test from figure 3.1 will give a preliminary qualitative explanation of what kind of result is

desirable.

•31

"lltU-of-p!;II1l.:((lad" 6IXJ;-.I

10001'1

Test 1

(a)

Test 2

(b)

Figure 3.1 - Loading Cases

Test 3

(c)

•

Test 1 consists of a IOOON in-plane force applied vertically up on the bottom of the head

tube while the bottom bracket and the rcar dropouts are rigidly fixed. as shown in figure

3.I(a). Test 1 gives a measure of the static response of a frame under loading from the

front fork due to a bump in the road. A satisfactory result for this test wouId be a relatively

compliant movement that wouId help minimize the force genemted by the impact of the

front wheel on a bump in the road which is subsequently tr.tnsmitted to the rider's arms.

Attempts to minimize this input foree have been implemented in recent years by the

installation of front spring or hydr.tulic suspensions on the front forks of mountain bikes.

Although this type of suspension would not be necessary for a road frame used in nonnal

conditions. a moderate in-plane resiliency is desirable.

Test 2 consists of a 600N load applied at the head tube in the out-of-plane direction while

the bottom bracket and the rear dropouts are rigidly restrained. as shown in figure 3.1 (b).

Test 2 is a measure of the lateral stiffness of the frame. whereby a small deflection indicates

a later.tlly stiff frame. which is desirable. This is desirable as under intense riding there is

out of plane. or twisting loads which are applied to the frame due to the rider's pedaling

action. Lateral or out of plane rigidity will prevent extreme defonnation of the frame and is

thus desirable. This test may a1so be called the "torsional rigidity of the front triangle".

Test 3 consists of a lOOON in-plane load applied vertically down at the seatpost. In this

scenario. the head tube and rear dropouts are fixed. as shown in Figure 3.I(c). The

displacement measurement is done in the direction of the applied load at the point of

application of the force. Test 3 is a vertical compliance test. A relatively large displacement

is favorable in this case as we again want to minimize the road-induced loads to the cyclist.

•

•

In a modilied triangular diamond shape structure. a way to appease the rider from a surface

bump could be to build a fmme like the Kestrel 500SCI (sec ligure 2.13) which climinates

the scat tube and thus would result in a more vertically compliant structure. Aiso. many

touring bicycle fmmes have scat mounted springs for the same reasons.

Since ail the tests are performed within the clastic limit of the material. the choice of load to

be applied is arbitr.ll)' as the load-displaeement curve is linear in the e1:l~tic region. The

above loads were chosen in order to obtain measurJ.ble dellections for the appropriate tests.

This series of tests is a satisfactory but non-exhaustive list that may be modilied or updated

in order to provide for a more complex and complete analysis in the future.

3.4 Experimental and Theoretical Techniques for Traditional

Frames

The 3 tests described in section 3.3 were simulated on 3 different models using FEA in

order to obtain stiffness values for tmditional geometry frJ.mes. The 3 models consisted of

one classical diarnond shape frJ.me that was modcled using isotropic shell clements. and

two classical frames modeIed using beam elements. A 52 cm chromium-molybdenum steel

frame built using Reynolds 501 tubing was modeled using isotropic shell elemenl~ and also

using bearn clements. Also. a 58 cm Trek 1100 frame made of 6061 aluminum tubing was

modeled using bearn elements only.

The experimental measurements on both the steel and aluminum frJ.mes were performed on

a specially built testingjig developed at McGill University. The jig consists of a rigid box

structure made of rectangular members with a large cross sectional area in order to restrict

the jig to minimal defleetions comparcd to those of the bicycle frame. Different points of a

bicycle frame can be ftXed to the structure using attachmenl~. thus creating fixed boundary

conditions for the test. Hydraulic cylinders were attached to the testingjig in order to apply

loads to the bicycle frame. By varying the placement of these hydraulic cylinders. load can

be applied in any axis. and at aImost any point on the bicycle frame. The applied load is

measured by calibrated load cells placed between the hydraulic cylinders and the load

application points on the frame. The displacements at the different locations arc measured

using dial gages. Figure 3.2 shows the testing jig used to test the frames.

(3.1 )

•

Figure 3.2 - StatÎC Bicycle FrJ.lTle Testing Jig.

The load cells consisted of 4 strJ.in gauges mounted to fonn a wheatstone bridge on a

rectangular picce of steel. The size of the steel picce was chosen so that at the minimum

expected load the steel would strain cnough to generate an appropriate bridge output. Also,

the steel cross section was chosen to be sufficient so that the induced stresses would be

below the yield stress at the highest expected load. The load cell dimensions were 13mm

by 13mm with a 6mm hole drilled through it. Hence at a load of 2000N (l\vice as high as

the highest load expccted with these tests) the stress in the steel will he:

F 2000Ci =- = ( ') 14.2MPaA 132 _ ;r :6'

From equation 3.1, the value of 14.2 MPa is well below the 250 MPa yield of low grade

steel. The next step is to make sure that the bridge output will be sufficient, even in the

low rJ.nge of the loads to be used. An analysis for the determination of the bridge output al

a 10ad of l00N is perfonned, as l00N will be considered as the lowest 10ad required to be

measured during the tests.

•l00N

CiIlJON = , = 0.71MPa140.7mm"

(3.2)

• The approximate str.lÏn value is:

(j 0.71MPaE=-= 3.43 X 10-'1<>

E 207GPa

Using the wheatstone bridge fomlUlas [57].

dR- = ~all~el(/("tor x ER • • J'

For this bridge the gauge factor is 2. hencc

dR _ ") a = 6 86 10-°"-_. XE • XR

and

34

(3.3)

(3.4)

(3.5)

(3.6)

•

where E is the supply voltage. Hence assuming a 5.0 volt source.

Eo =0.25x6.S6x lO-Il<> x5.0 =S.575 x lO-Il<>Yolts (3.7)

and the bridge output signal will be:

ED.".I = 2 x (1 +Jl) x ED (3.8)

The resulting voltage is thus

ED.",w' = 2 x (1 +0.3) x S.575 x 10-ll<> = 2.23 x 10-05 volts = 0.022mY (3.9)

From equation 3.9 a wheatstone bridge output of 0.022 mV is expected at lOON, hence

0.220 mV at 1000 N. These voltages can easily be measured using a conventional

voltmeter. If the wheatstone output would have been insufficient. it would have been

possible to amplify the sig:tal, but this was not necessary.

Although the above analysis provides an approximation of the expected output from the

load cell, the cell required calibration before accurate load measuremenL~ could be

performed. The load œil calibration was done with a Chatillon TCM 200 tensile tester

equipped with a calibrated load cell. The cells were powered by a constant 5.0 volts OC

voltage and the resulting wheatstone bridge output was read from a Keithley 195A digital

multimeter. Figure 3.3 shows the calibration curve used for the load cell. This curve gives

an average traDsfer function of4350 N/mV. This transfer function gives a bridge output of

0.023 mV for a 100 N load compared with the 0.022 mV, found analytically.

//

/

/V

//

//

300

200

100

oo 0.05 0.1 O., 5 0.2 0.25

Wheatstone bridge output (mV)

Figure 33 - LlKld CclI Calibration Curve

1000

900

800

700

600z-g 500

.3 400

•

3.5 Finite Element and Experimental Results

Table 3.1 shows the tinite clement and expcrimental results as obtained for the 3 ditTerent

tests on the different fmmes. For the experimental results. the values obtained 'U'C an

avemge of 3 runs which were donc for eaeh test.

F.EA. Experimental

. Steel-beam Steel- shell Al.-beam Steel Aluminum1·

No. of 10 ISOO 10 NA N.A.

cléments

Weight(kg) 1.46 1.53 1.2S 2.0S I.S0. C •

TEST! 0.27 0.32 1.00 0.40 1.14

(mm)

TEST 2 22.9 25.6 32.0 24.9 34.1

. (mm).. .T~T3·· . 0.05 O.OS 0.001 - -

.. (mm) ..•.

•Table 3.1 - Finite Element and Experimental Resull~ for Metallic Fr.unes

•

•

% error between 9é crror bctwccn CJé crror bctwccn

experimental and experimental and experimental and

Steel-bcam modcl Steel-shel! model A!.-beam model

TEST 1 S\l 25 1-1

TEST::! 'i>.7 :'.7 6.5

Tabh: 3.:' - EITors Between the Finite Element and Experimental Results

Numerous observations ean be made from tables 3.1 and 3.:'. In test :.. the difrcrenee

between the expcrimental and FEA results is less than 7% for hoth the stecl and the

alumil1lll11 frame. However. for test 1. the FEA :md experimelllai results dilTer by a larger

amounl. En'ors up to :'Oç~ ean be detecled hetween the linile c1emenl and expcrimelllai

results. An interesting aspect to note is lhat the experimental results :U"C consistentlv higher~ . -

than the FEA results. A possible explanation for this would be a slight Iack of rigidity in

some parts of the jig (possibly the boundary conditions) which would contribule in giving a

larger displaccment for the same load in the experiment:ll results compared with the linite

clement ones. This effect is mueh more important for test 1 than for test ::! as the

displ:\eement for the former are much snml!er. The movement of some of the eomponems

of the jig (retaining plates. bolts. nuts) is suspected lo t:lkc pl:lce at the initial load

application strengthening this possibility. Test 3 was impossible lo perfonll expcrimentally

because of the geometry of the jig. However. it secms that the dilTerence in lhe FEA

results = much more evident than for the other tests. The most probable explanation for

this behaviour is that the beam clement models are not suitable for this particular in-plane

load. Aiso. the larger diameter of the a1uminum tubes comp=d with the sleel ones might

lead 10 a much stiffer structure for this type of 10:ld and mesh. yielding results for test 3

which arc very different for each mode!.

The comparison between the FEA and experimemal results is good considering the errors

that could arise l'rom a number of sources such as the difticulty in modeling the exact

intricate shape of a bicycle fr.une, the modeling of restmints by FEA, and inherent errors

involved in experimental mea.~uremenl~. The fact that experimental resull~ match the FEA

to some extent gives confidence in other FEA results. As the goal was to comp= fr.unes

without actually building them, experimental testing on existing fmmes confimls the idea

that FEA testing can replace experimental testing. Another important observation is that the

steel fr..lme, which is modeled using both beanl and shel! clements. gives results which =

appreciably close to each other. It could thus be concluded that for a classical fr.une with

•

•

37

tlInular g.:om':lry;' mu.:h simpkr and qui-:k.:r sliffn.:ss analysis using k;II11l'1.:m"nts "an nl'

don.: in ord.:r 10 ontain approximaI': r.:sults for som.: l.:sl simulations. '\':\l·l1hd"ss. il

should n.: r.:m.:mn.:r.:d lhal if;1 .:ompkl': Slr.:ss analysis is r.:quir.:d. lh.: n"am I110dd \\'llUld

nol n.: suflki.:nt to pro\'id.: lhis informaI ion.

ln addilion 10 çomparing a.:lual tradilional f!"am.:s to Ih.:ir Iinil.: d.:m.:nt mod.:1s. olh.:r

Iradition~li sl.:d fram.:s \\'.:r.: st;lli.:ally l<:st.:d on lh.: I.:sling jig. This fUl1h.:r l<:sling of sl.:d

fr;un.:s \\'as don.: in ord.:r to ontain basdin.: \'alu.:s for lh.: difll:r.:nl l.:sts in ord.:r to

çompare \\'ilh the futur.: çarnon liner fr.unes buill as a r.:sull of lhis proj.:.:!. T.:sI 1 and 2

\\'.:r.: lhus p.:rllmn.:d on t\\'o olher sl.:d fram.:s. Th.: lirsl on.: is a Colnago Sport fram.:

which uses Columnus Aelle lubing. This frame is a light ~md Ilcxible Ilalian radng fram.:.

The second is a high quality Rocky ivllllll1tain frame buill l'rom T.mge Prestige tubing. This

mountain bike frame is made l'rom one of the besl slcd tlIbing malerials a\'.ül~lble .lI1d Ihus

is considered as one of the best slecl mOlll1lain bike fr.lmes on the mark.:!. Tabk 3.3 shows

the results obwined for tesl 1 and 2 Il)r the two fram.:s describco abo\'e. Induded in the

lable arc resulls l'rom lhe other sted frame (Reynold 50 t ) which was .:arlier comp;lred to its

Iïnite cl.:menl modcL

From table 3.3. obser\'e that the Rocky MOU:llain frame. which uses Ihe Tang.e Prestig.e

tubing. is by far the stiffest in the mlt-of-plane direction as conlïmled by test 2. An

interesting aspect to consider is th'lt. at the :;;lme time. this Ihlme still offers the most

compli'lOl head tube motion .LS shown by lest 1. This re\'eals a \'ery weil designed frame.

as il combines lhe du'll attributes of being compli'lOl in-pl.me and stitT out-of-plane. It is

this trend Chigh olll-ol~plane sliffness and low in-plane stilTness) which will be .1 goal for

the design of the c'lrbon tïber frames.

Bicycle frame Tubing material Test l Test 2

(mm) (mm)

Chabot Frame Reynolds 501 .40 24.9

Colnago Columbus Aelle .31 27.8

Rocky Mountain Tange Prestige .53 18.6

Table 3.3 - Steel Fmme Test ResuIls

•

•

38

ln chapter -1 these results will bc compared with the composite prototypes whieh will bc

constructed. Even though these traditional frames are nN the best racing frames on the

market. they are of reasonable quality so as to provide an adequate bascline upon which the

composite frames should be improved upon.

•

•

39

Chapter 4

Composite Frame Design

4.1 Introduction

This chapter will focus on the design and finite-element analysis of the composite frames

developed during this project. This is the core of the research. ln order to set goals for this

study. a number of design criteria were set forward. The first criteria is low weight. A

fmme weight on the order of t500g should be sought. This is slightly tower than other

composite frames on the market and in the sarne range as the lightest alurninum frames

available. The second design criteria is to obtain a frame with the appropriate stiffness at

the appropriate locations. The head tube and bonom bmcket stiffnesses should be as high

as the stiffest f=es on the market (such as the ones sarnpled in chapter 3). The frame

should also be compliant in the vertical direction in order to help dissipate road

irregularities. These criteria will guide the design and construction of the composite

monocoque f=es.

4.2 Finite-Element Analysis of the Composite Frames

The finite-element analysis of the monocoque bicycle f=es was performed using SDRe's

l-DEAS fmite-element software [58]. This software is particularly appropriate for this type

of structure as il incorporates both a very good composite larninate modeling section with

advanced geometric modeling capabilities. l-DEAS uses a standard classical larninated

plate theory with an option to calculate additional interlaminar shear stresses. The laminate

modeling section directly computes ail of the stiffness matrice.~ which are inherent to the

use of materials with orthotropic material properties (i.e.. composite materials). The

calculations and manipulations of the stiffness matrices for each larninate are very tedious.

•40

so detailed analysis of a composite bicycle frame using any method other than using finite­

element analysis is practically unthinkable. The following sections will describe the

important considerations of the finite-element analysis. namely geometry. laminate

configuration. loading. boundary conditions and results.

4.2.1 Geometry

The geometry of the frames was the fmt parameter to be studied. The fmt step in

geometry development was to invent as many possible geometries based on observation

and engineering intuition. From the initial geometries, three were kept after prelirninary

stress and deflection analysis was performed [59]. The three frame geometries studied are

shown in Figure 4.1

•

Prototype 1 Prototype 2 Prototype3

Figure 4.1: Frame Geometries ofThree Composite Monocoque Prototypes

The geometry of the frames must also respect rule 49 of the Union Cycliste Internationale

(UCl) which sets forth technieal specifications for bicycle frames for use in intemational

cycling competitions [60]. Figure 4.2 shows the specific dimensions which are regulated

by rule 49 and Table 4.1 shows the dimet:lsions of the 3 composite frames and how they

obeyed the rues.

In addition to the specifications outlined in Figure 4.2 and Table 4.1, no features on the

frame should serve as to reduce the drag or to accelerate the propulsion by any means, such

as li wind protection shield. or other devices that serve only an aerodynamic purpose

without being structural. The other restrictions of rule 49 are automatically met by the use

of normally available bicycle components.

41

18

1A

F:::::::;::1==::::::"~:?i··

1 r~\i1 ~ •, \

_~__ 1

~\ /

1c

•

E

Figure 4.2 : UCI Rcgulated Dimensions

., .. IJCI Rule Prototype 1 Prototype 2 Prototype 3.. AB (cm) 54-75 58 57 64

AD(cm) .. 24-30 30 28.5 27"

,~.> ' " .. .::~5(cm):' 35·55 46 41 44

cEF'(cm).. ····· <200 173 168 178k ~: ",' ~:: . ,;~,": '

Table 4.1 : Prototype Dimensions

•

The shape of prototype 1 was chosen because it possesses a similar geometry to that of the

LOTUS (see Figure 2.17). The thickness of the main part of this frame was 75 mm. This

results in a structure which is quite bulky. but pr~vides excellent torsional and out-of-plane

rigidity. Prototype 2 models a beam which extends from the rear dropouts to the top of the

head tube. This geometry is new and original and no other composite fr.une on th(' market

possesses a geometry similar to il. The frame thickness is 50 mm. This reduction in

thickness was made in order to Iower the aerodynamic drag and make the frame more

aesthetic. The reduction in thickness from 75 mm to 50 mm will reducc the inherent

rigidity but with an increase in number of plies. the lateral rigidity may be made equivalenl.

Prototype 3 is actually a modification of the Bearn bike (see Figure 2.15) which is on the

market now. The modification is that prototype 3 contains a seat beam; a feature which is

not part of the original design. This modification aIIows a reduction of the lateral sway and

vertical movement associated with the cantilevered scat design of the beam frames. A

•

•

42

stress and failure analysis was perforrned on these three models. The three frames were

modeled using thin shell triangular and quadrilateral clements. Thin shell elemenL~ were

used as they arc appropriate for modeling the thin structure of a composite of large surface

area. Also, thin shell elements are used by default by the laminate modeling section of the

software as they best represent a thin composite layup. The FEA models do not contain an

internai core that eonstrueted prototypes have. The introduction of the internai core was

donc as an aid to fabrication and should have only a small influence on the stress state thus

it can be ignored in the mode!. Prototype 1, 2 and 3 contain respectively 2260, 1558, and

2156 thin shell elements. The different prototypes also used other types of elements in

order to model the frame. For example rigid elements were used in order to apply forces or

restraints at locations where they actually occur. These rigid beam elements represented

handlebars, pedals, and fork stems. This perrnits the complete transmission of actual loads

to the frame without any losses through the members.

4.2.2 Material and Laminate Configuration

The materials used for the modeling and construction of the frames are unidirectional and

woven high strength carbonlepoxy prepreg. The woven material was modeled in the finite­

element software as being one layer with equal rnaterial properties in the x and y-planar

material directions. The unidirectionallayer was modeled with orthotropic properties. The

material properties used for the fmite-element and failure analysis are shown in Table 4.2

[61]. Laminates for different elements of the 3 prototypes were modeled using the laminate

modeling capability of the software. The 0° direction, i.e., the x-axis of a local coordinate

system coinciding with material orientation used for the laminate construction, is taken to

be the direction of a vector going frorn the rear dropouts to the top of the head tube. From

the given 00 vector, the finite-element software automatically generates a corresponding

vector for each element on the surface of the frame. The x-direction, corresponding to

material orientation, is J:!us different for each element of the frame. The 90" direction, i.e.,

the y-direction for the local material orientation, is again in the plane of the elements,

perpendicular to the x-axis according to the right hand rule with the z-axis pointing outward

from the surface. Note that throughout this research the stresses are given in terms of this _

coordinate system. Hence, for example, the x-direction stress is a stress along a direction

corresponding to the 0° vector of a certain element, and the shear stress is in the plane of the

element A global cartesian coordinate system will aIso be used and will have its -x-axis

along the direction ofmotion ofa frame with wheels, with its y-axis vertically up. Figure

• 4.3 shows the global x-y axes. the global (f vector and thc local (f vector for a certain

clement of prototype 1.

, , , • , , 1 l , , • ,

1 •••• ,., 1..

, . ,. ,, ,,,,, ,

Y-Globi>1•~GIObi>1

Figure 4.3: Direction of the 0° Vector.

The laminates diseussed in the following subseetions arc the result of an evolutive study in

which many types of laminates were attempted in order to develop a close to optimum tiber

orientation for each case in terms of strength. stiffness and case of fabrication.

'Unidirectional carbonlepoxy

,;:,. '>, ,~,;,_:<_ :', "AKZOHTA7-LlM20

Woven carbonlepoxy

CFS OOl-LTM22

1724MPa

93.1 MPa

0.263 kg/m-

562MPa

405 MPa

0.28 mm

78.2MPa

3.17 GPa

67.0 MPa

65.6 GPa

0.435 kg/m-

•Table 4.2: Material Propcrties for Unidireetional and Woven Materials Used in this Study

[61]

•

•

44

4.2.2.1 Laminate Configuration of Prototype 1

Prototype 1 includes 5 differentlaminates containing woven and unidirectional material and

corresponding 10 layups used at different locations. It should be noted that this particular

prototype was modeled and constructed only as a verification of the finite-element analysis

results and construction method. Hence this particular framc couId not bc used in a riding

or racing situation as it was not designed nor conccived to do SO. Unidirectional material

was used in conjunction with the woven material in certain high load arcas as

reinforcement. The regions of high loads were matched with the regions of material

overlap since those regions have more material to support the load. The overlap regions

were at least 25mm which weil exceeds the required load transfer length of only severa!

millimeters. Hence overlaps actually worked as reinforcement. The main front part of the

frame was modeled and made of 2 layers of woven material. The layup changed to 4 layers

in the overlap regions. Also unidircctional reinforcement was added to regions wherc 2

and 4layers of woven material was already present. Thc last layup is in the rear region of

the frame inside the weil where the rcar wheel is located. This region contains only one

layer of woven material. Hence, for this frame, the 5 different laminates include:

1- 1 layer of woven material

2- 2 layers of woven material

3- 21ayers ofwoven material + overlap (4layers woven)

4- 2 layers of woven + unidircctional

5- 2 layers of woven + overlap + unidircctional

Figure 4.4 shows the mesh and the different laminate locations for prototype 1. The

numbers in Figure 4.4 correspond to the laminate numbcrs enumerated above.

•

•

45

Figure 4.4 - Finite-Element Mesh and Laminatc Regions for Prototype 1

4.2.2.2 Laminate Configuration of Prototype 2

Two sets laminates were considered for prototype 2. The first laminate used only

unidirectional material applied on the mode!. It contained a [0/90],6-layer laminate in the

low load regions built up with overlaps to a ID-!ayer [°/9°/°], laminate in higher load

areas. This laminate was not adopted for construction because after the construction of

prototype 1. it was realized that the use of unidirectional material on a structure as complex

as a bicycle frame was very problematic. The unidirectional material did not conform weU

to double curvatures and hence cannot be used exclusively in the construction of a frame.

It was thus allempted to model prototype 2 with woven material only. because even if the

unidirectional reinforcement provides beller stiffness and strength. it is believed that the

construction process would be accelerated with the use of only woven fabric. Hence

another laminate using woven material was developed. The laminate modeled for this

prototype was made of 3 layers of woven material in low stress areas and a buildup to 6

layers in the overlap regions. Again the overlap regions were made to correspond to higher

10ad areas. Prototype 2 was also modeled using 45° woven reinforcement in sorne areas as

will be discussed later. The 45° reinforcement in the head tube. bollom bracket and rear

•

•

46

dropout regions was used in order to provide reinforcement in those critical areas as weil as

increasing the torsional rigidity in those regions. Figure 4.4 shows the finite-element mesh

and different laminate regions for prototype 2. Hencc for Figure 4.5. the 3 different

laminates or: the frame correspond to the fo~:owing code:

1- 3 layers woven

2- 3 layers woven + overlap (6 layers woven)

3- 3 layers woven + overlap + reinforcement (8 layers woven)

Figure 4.5 : Finite-Element Mesh and Laminate Regions for Prototype 2

4.2.2.3 Laminate Configuration for Prototype 3

The laminate for prototype 3 was modeled using unidirectional material only. A [0/901,

laminate is used with overlap reinforcement making the laminate a [0/90/02), in critical

regions. Figure 4.6 shows the location of the two laminates applied to prototype 3. Region

1 on Figure 4.6 has a [0/901, laminate while region 2 has a [0/90/02), laminate. This

frame was only designed and developed on computer and was not constructed as part of

this research project

•

•

47

Figure 4.6 : Finite-Element Mesh and Laminate Regions for Prototype 3

4.2.3 Loading and Boundary Conditions

The loading and boundary conditions for a study of this type arc very important in order to

obtain realistic and useable resull~. A bicycle frame in motion is a complex loaded

structure. In order to perform a reasonable stress analysis. it is important to choose a load

case which closely represents true riding conditions. A~ track racing or time trial racing is

the discipline of interest. and is performed under controlled road conditions. only rider

induced loads were considered here. Although this assumption is quite valid for track

racing. it certainly is not for mountain biking. Aiso. a load case where only one load is

applied ::t a specific location. for example at the pedals. with stress and displacement

patterns obtained throughout the frame is too simplistic and cannot realistically he used for

design. An analysis of this type would only inform the designer about the specific

response to a certain load and not the response of the frame to a riding situation. The load

case chosen for this study contains loads applied to the frame by a racer ridinr on a flat

surface at SOkm/hr developing an average power of 400W. This load case is a static load

case obtained al the point during the pedaling stroke where the loads arc at a maximum.

•

•

48

hence this study is for the worst case static scenario. No dynamic analysis was performed

during this research. This load case was calculated analytically and corresponds closcly to

what has bcen measured for the maximum loads in another study where loads at different

application points were measured as a function of cnl11k angle [62]. Loads during this

study were calculated for a conventional geometry 56 cm fmme. thus small corrections

would have to bc made in order to use it for a different size bike. This particular load case

is different from those used in other studies as it considers the non-negligible effect of the

chain and thus renders the loading situation non-symmetric with respect to the major

vertical plane of the bicycle. Hence it is not possible to use symmetry to reduce the numbcr

of clements on the fmme. It is bclieved that this load case reflects reality and is a good

starting point for design. The following is a complete description of the load case

derivation.

4.2.3.1: Starting Hypothesis of Load Case Derivation

-Mass of cyclist: 80 kg hence W=785 N

-Loads on the handJebars by the arrns are unknown

-Angle of the arrns with the handJebars is 45°

-Speed of the bike is 50km/hr = l3.88m1s

-Aerodynamic coefficient: C, = 0.83 [63]

-Surface of the bike-eyclist assembly S = 0.3m2 [63]

-Flat terrain

-Wind speed=O

4.2.3.2: ProbIem Steps

-Caleulate the power expenditure of the cyclist

-Calculate the loads on the pedals from the input power

-Isolate the bicycle and eaieulate the loads on the wheels

-Isolate each wheel

-Calculate the Ioads on the frame

4.3.3.3: Powers InvoIved

-Power developed by the cyclist: PCYc!;M

49

• -Power dissipated by the chain transmission is negleeted ( a chain transmission is typically

98% efficient) [64]

-Power lost duc to air resistance is t'""

-Power dissipated by rolling resistance is neglccted

-Power dissipated by the contact forces perpendicular to the roads arc neglected

(4.1 )

(4.2)hence P""", + P,,;, =0

P~'~'di'i = -P;lir= FOIir V= 0.5 p C, S V' V

= 0.5 x 1.19 x 0.83 x 0.3 x 13.S8~ x 13.88

= 400W

Then at constant speed applying the l;inetic energy theorcm

Plut'"~ = dE/dt = 0

Wherc '1= Riding Velocity= 50 km/h = 13.88 mis

C, = Aerodynamic coefticient = 0.83

S = Frontal arca = 0.30 m'

p = Air density = 1.19 kg/m;

Forcomparison. reference [65] shows a mcer riding at 12. 1mis (43.6 km/hr)

corresponding to a tr.lctive power of 373W and from [66] a time trial power output for a

40.22 km record performance at an avemge speed of 13.6m1s (49km/hr) produces a power

expenditure of more than 373W.

•

•50

4.2.3.4: Calculation of pedal loads

Isolate the chain drive

r=360~

55tœlh

•

r=25mm12 tœl h

Figure 4.7 Chain Drive

The circumference of the back wheel is 2261 mm, hence at SOkmlhr (13.88m/s) the rear

12 tceth cog tlIms at:

V/r = 13880/2261 = 6.14 tumsls (4.3)

hence the front chain ring rotates at

(12 teethl55 teeth) .. 6.14 tumsls = 1.39 tumsls

or w = 8.73 radis

From the total power (P) of 400 W. the couple C at the bottom bracket is related to the

power delivered by the cyclist by the following relation, where IV is the angular velocity

P=Cw = 400W (4.4)

orC = P Iw =400/8.73 =46 Nm

Agam for comparison [67] shows 35Nm for 373W at 105rpm and increasing torque for

lowerrpm.

If the crank arms have a radius r of 170nun, the total force exerted on the pedals will he:

• C/r=46Nm/O.17m =271 N (4.5)

51

•

where we a,'sume tha! the r.\cer pushes down on the right pedal with 75% of his force

while pulling up on the left pedal with the remaining 25%. The downward force with the

left pedal will be 203N (Fp) while the upward pull is 68N (Ft) as shown in Figure 4.8.

This a,'sumplion is intuitive but could ea,~i1y he justified and shown to he dose to reality if

an appropriate study on this subject were performed.

4.2.3.5 Considering the Complete Bicycle

The forces present are:

-The weight of the rider (p)

-The pulling forces on the handlebars (T)

-The wind resistance (Fwlnd)

-The loads on the pedals (Fp and Ft)

-The loads on the wheels (R, (front wheel) and~ (rear wheel))

T

Figure 4.8 : Forces Acting on the Bicycle

F=mA

Fp + Ft + Fwind + T + P + RI + R2 = 0 (4.6)

x-direction: Tx + RIx + R2x + Fwind x =0

• Tx + Rix + R2x + 29 =0

y-direction: Ty + P + Fp + Ft + Rly + R2y = 0

Ty - 785 -203 + 68 +Rly + R2y = 0

Ty -920 + Rly + R2y = 0

(4.7)

(4.8)

52

And the moment equatÏon. taken about a moment a;l:is in the z-directÏon at the bottom

bmcket axis is:

-0.1 P + 0.170 Ft + 0.170 Fp + 0.3 RIx + 0.3 R2x + 0.42 R2y - 0.68 Rly - 0.62 Tx-

0.49 Ty - 0.3 Fwind = 0 (4.9)

-33 + 0.3 RIx + 0.3 R2x + 0.42 R2y - 0.68 Rly - 0.62 Tx - 0.49 Ty - 0.3 Fwind =0

Isolating the front wheel:

•

Figure 4.9: Front Wheel Free Body Diagr.trn

where : FI is the load applied by the wheel on the fr.trne.

RI is the load applied by the ground on the wheel

RIx + FIx =0 (x-dir.)

Rly + Fly = 0 (y dir.)

RIx * radius ofwheel = 0 (moment eq.)

hence Rlx=O (4.10)

•53

Isolating the rear wheel:

Figure 4. 10 : Rear Wheel Free Body Diagnull

Where : F2 is the load applicd by the wheel on the fr.une

R2 is the load applied by the ground on the wheel

R2x + F2x = 0 (x-dir.)

R2y + F2y = 0 (y-dir.)

R2x * radius of wheel + C = 0 (moment eq.)

where C is the chain couple which was found to bc equal to 46Nm using equation 4.4.

hence:

R2x = -46 Nm 1350mm

R2x=-131 N

and: F2x = 131 N

Assuming the force on the handiebars to bc at 450 to the horizontal.

Tx=Ty

(4.11 )

(4.12)

Using (4.7). (4.8), (4.9). (4.10), (4.11), (4.12) . solve for ail the parameters to get:

From (4.7) Tx + Rix + R2x + 29 =0

Tx + 0 -131N + 29 = 0

Tx= 102N (4.13)

•From (4.12) Tx=Ty= 102N (4.14)

• From (4.8) Ty -920 N+ Rly + R2y = G

102 N - 920 N + Rly + R2y = 0

Rly + R2y = 818 N (4.15)

54

From (4.9) -33 + 0.3 Rix + 0.3 R2x + 0.42 R2y - 0.68 Rly - 0.62 Tx - 0.49 Ty - (0.3

* Fwind) = 0

-33 + 0 -(131*0.3) + 0.42 R2y - 0.68 Rly - (102*0.62) - (102*0.49)­

(29*0.3) = 0

-33 - 39.3 - 63 - 50 - 8.7 + 0.42 R2y - 0.68 Rly =0

-194 + 0.42 R2y - 0.68 Rly =0 (4.16)

Using 4.14. equation 4.8 becomes Rly = 818 - R2y (4.17)

Using 4.17, equation 4.16 becomes -194 + 0.42 R2y - 0.68 * (818 - R2y) =0

-194 + I.I R2y - 556 =0

I.I * (R2y) = 750

R2y=682N (4.18)

and from 4.17 and 4.18 Rly = 818 - R2y

Rly = 818 -682

Rly= 136 N (4.19)

•

Hence in conclusion we have from 4.10. 4.11. 4.14. 4.18 and 4.19

Rlx=O

R2x=-131 N

Tx= 102N

Ty= 102N

R2y=682N

Rly= 136N

(4.20)

(4.21)

(4.22)

(4.23)

(4.24)

(4.25)

• 4.2.3.6 Calculation of the Frame Torsion Forces on the Handlebars

T1y

Figure 4.1 1 : Handlebar Forces

55

Tlx + T2x = 102

TI Y+ T2y= 102

(4.26)

(4.27)

Moment equation about bicycle centerline at pedal axis:

X-dir: Fp * 80mm - Ft * 80mm· T2y*200mm + Tly*200mm =0

68 * 0.08 + 203 *0.08 + T2y*0.2 - T1y*0.2 = 0

21.6 + T2y*0.2 -Tly*0.2 = 0 (4.28)

•

Y-dir: T1x * 0.2· T2x * 0.2 =0

Hence Tlx =T2x

And from (4.26) and (4.29)

Tlx = T?..x = SIN

from (4.27) and (4.28).

21.6 + (102 -Tly) * 0.2 - Tly*0.2 =0

42 - Tly * 0.4 = 0

(4.29)

(4.30)

• hencc Tly = lOS N

and from (4.27)

T2y = 102 - 105 =-3

T2y= -3N

The complete load case is now shown in Figure 4.12.

Wind Load

-Z 52N3N

sON ........l tlOSN

~-';:Ic 66Nt34IN

t~341N 1906N

Figure 4.12 - Riding Load Case

(4.31 )

(4.32)

56

•

The loads shown in Figure 4.12 were applied to the iinite-clemcnt tnin shell nodes cither

dircctiy or through the rigid bearn elements used at the handlebars and pedals. In the

regions of the seat and rear dropouts. the loads are divided up ..nd applied to many nodes

directiy on the shell mode!.

4.2.3.7 Boundary Conditions

The restraints anempted to modr-I the boundary conditions on a riding bicycle frame as

c10sely as possible. The frame was restrained al the botlom of the front fork as weil as the

left and right rear dropout. These are the only points where the frame ;~ in contact with

components that are directiy in contact with the ground. There are no more locations were

restraints could he implemented.

• Fix~ù YandZ translationFix~d X andy rotation

\Fix~ù X. y anù ZtranslationFix~d Y rotation

57

Fix~d Y.and Z trJn,lation.-P"Fix~d Y rotation

Figure 4. 13: Riding Restraint Locations

The restraints shown in Figure 4.13 arc summarizeù in Table 4.3. This rcstrJint set has

been previollsly used in otber bicycle frame stress slUdies [621. The global coordinate

system used is shown in Figure 4.! 3.

[n the above Table. * denotes a ltxed degrce 01 freedom.

Table 4.3 : Riding ResmlÏnts

x y Z X rot. Y rot. Z roI.

Bottom of front tork * * * *Lefi rcar dropout * * *

. Right rear dropout * * * *. ..

4.2.4 Stress Analysis Results

•

Stress anaIysis is essential in many ways. It a110ws the determination of the stresses in the

different Iayers and thus assur"s that the stress levels arc below the a1IowabIcs. AIso. it

aBows the visualisation of the different high stress arcas so that modifications can bc

implemented. The stress analysis was performed using the Ioads and boundary conditions

described in section 4.2.3. Classical Iaminated plate thcory was assumed. and stresses

were found in each of the laminatc Iayers. Nom1a1 stresses in the x· and y-directions as

weB as the in-plane sheur stresses were obtaincd.

•58

4.2.4.1 Prototype 1

Tht: maximum strt:sses for prototypt: 1 wt:re (lbtaint:ù for t:ach layer of each laminate. The

stresses arc tabulateù in failure index fonn (stress dividt:d by strength as per the maximum

stress criteria [68 D. The maximum stress criteria is justitied in this study because one stress

(shear stress) is the dominant stress which may cause failure. A l"ailure index of 1 means

failure in the material. while a failure index of 0 means no stress al ail. The factor of safety

is then the reciprocal of the failure in':ex. The failure index for lhis prototype was cakulated

with the f::tilure stress of the material at the location of the maximum stress for each layer.

The x-direction refers to the material orientation direction in the plane of the clements that

was c!etined from the rear dropouts to the head tube. The y-direction is a direction

pcrpendic:ular to the x-direction in the plane of the clement. Table 4.4 shows the maximum

l"ailure indices for each material failure mode in each ply.

"Umdlrectlonal layer

Table 4.4 : Maximum Failure Index for E:ich Layer of Prototype 1

Xtension Xcomp. Ytension Ycomp. XYshear

Ply 1 0.092 0.196 0.049 0.080 0.493

Ply 2 0.043 0.168 0.085 0.168 0.628

Ply 3 0.042 0.193 0.082 0.144 0.633

Ply 4 0.031 0.067 0.083 0.083 0.494

Ply 5'" 0.047 0.225 0.004 0.008 0.280..

It is interesting to note trends fr('m Table 4.4.

prototype arc due to in-plane shear stresses.

contours in ply 3.

The largest failure indices for the tirst

Figure 4.14 shows the xy-shear stress

•

59

RidinglœdsMateri2l1 frame of referenœXY-sbœr stress in ply 3

50

2S

MPa

o

-50

Figure 4.14 : XY-Shear Stress Contours for Prototype 1. Layer 3

1

Figure 4.15 : X-Normal Stress Contours for Prot<:>type 1. Layer 1

From Figure 4.14. note that the largest shear stress region occurs near the edge of the front

curvature of the frame. Two other large stress regions occur near the bonom bracket and

the rear curvature. As shear stress is reduced by the addition of 45° layers. from this.

analysis. it can be seen that more 45° layers would be needed in the front and back

curvature regions. This observation corresponds with existing practice for tubular carbon

fiber frames where the down tube is made mostly with 45° layers in order to resist down

•60

tube torsion [21]. Hence for this first prototype. with this particular laminate and under

these riding loads. the in-plane shear stresses are the highesl.

Figure 4.15 shows the x-direction fiber stress in ply 1. The magnitude of the x-stress on

this frame is higher than the xy-stress. but considering the abiliry of composites for

carrying loads in tension. the failure indices for this malerial direction are much lower. The

most important aspect to consider from Figure 4.15 is that the high stress region is

conccntrated near the bollom bracket and that the rest of the frame is under an almost

constant Slate of low stress. The distribution of the low stress evenly on the frame is a

geometric allribute of a specific design. Hence only reinforcing the bollom bracket region

(although not necessary in this case for this specific stress component) would be sufficienl.

It is also interesting to note the thin region of higher stress going diagonally down from the

head tube region toward the rear dropouts. This general direction corresponds to the

bending load path for a bicycle frame so it is interesting to see that this physically intuitive

aspect shows up in the finite-element results.

PLV HO: 1

15.04E+()7

Figure 4.16: Y-Normal Stress Contours for Prototype 1. Layer 1

Figure 4.16 shows the y-stress in ply 1. As ply 1 is made from woven material. the y­

stress is again a fiber stress. As seen from Table 4.4. the magnitude of the y-stress is

•

•

61

much Jess than the x-stress for ply 1 shown in Figure 4.15. Again. a fairly uniform state

of stress is observed throughout the frame with larger stress regions observed in the baek

of the seat region and near the bOllom br.lcket.

Figure 4.17 shows the out-of-plane displacemenl~ under the riding loads and boundary

conditions. The out-of-plane displacement varies from 1.37mm in the positive z-direction

(out ofpapcr) to 3.32mm in the negative z-direction (into paper). The top part of the frame

is essentially free of out-of-plime displacemcnt. On the other hand the bollom br.lcket

region and ovemll lower part of the frame is affected by out-of-plane displacement. As was

shown in chapter 3. the out-of-plane displacement should be restricted to a minimum to

prevent extreme defonnation in the frame. hencc if more reinforcement should be added, it

should be done in the areas of the frame near the bOllom bracket. Hence it is clear that in

the bottom bmcket region. geometric and larninate design is of utrnost importance.

0.001371

0.0000I33

-0.001443

-o.oo3'h&

Figure 4.17: Out-of-Plane Displacement Contours for Prototype 1

•

•

62

4.2.4.2 Prototype 2

Table 4.5 shows the m:Lximum failurc indices for the second prototype. again subjected to

the same loading and rcstr.lint set as prototype 1.

X tension Xcomp. Ytension Ycomp. XYshear

Ply 1 0.138 0.172 0.075 0.170 0.744

Ply 2 0.124 0.156 0.077 0.170 0.763

Ply 3 0.126 0.169 0.099 0.142 0.782

Ply 4 0.043 0.175 0.040 0.114 0.660

Ply 5 0.033 0.122 0.036 0.186 0.679

Ply 6 0.049 0.185 0.067 0.140 0.692

Table 4.5: Maximum Failure Index for Each Layer of Prototype 2

For prototype 2. the highest stresses were again duc to shear stresses but only in the region

of the bollom bmcket. espeeially on the left side of the bicycle where the chain is locmed.

Figure 4.18 shows the shear stresses in the bollom br.leket region. The shear stress varies

l'rom a positive value to a negative value within a small region. The magnitude of these

shear stresses being very high in this region. carcful laminate design has to bc

implemented. This is why the addition of reinforcement was eonsidered in some speeilie

regions. The addition of reinforcement will bc diseussed in this section. Exeept for the

large concentrated values of shear stress. the rest of the fr.ln1e is submilled to very low

values of shear stress. The same is observed for the x-stress (liber stresses) shown for ply

1 in Figure 4.19. Large values of stresses. shown by the darker regions. arc located in the

bOllom bmeket region where most of the load (l'rom the rider's legs) is introduced to the

composite structure. However. it is clcar l'rom the failurc indices that this fr.ln1e will not

l'ail duc to tensile or compressive loading of the libers.

63

•RidiIlg loadsMaterial frame of referenœXY-shear stress in ply 3

50

25

oMPa

-25

-50

-75

Figure 4.18: Prototype 2 - XY-Shear Stresses at Bollom Br.lcket Region. Layer 3

LOAD SET: 1 - Rl~JHC LQMDS~ OF' REF: HATERIAl.PLy STRESS - X HIH:-'.b6E

PLY HO: 1

1.21E+oS

9.JŒ+o7

6.64E+o7

J.92E+o7

,

~::I

:::1-'.66[..01

•

Figure 4.19: Prototype 2 - X-Normal Stress. Layer 1

Figure 4.20 shows the y-stress in ply 1. Most of the frame is subjected to very low y­

stress which is again a fiber stress as this is a woven material. The bollom bracket region

is again submitted a higher y-stress. From the above discussion. it is irnmediately evident

that the bottom bracket region is the most highly loaded and stressed and that it should be

•64

thoroughly considered both during design and fabrication of the frame. It is a region where

geometry, unfortunately docs not lend itselfto easy material application. This is especially

true for this prototype where the bouom br.lcket region seems auached to the rest of the

fmme in a way which may not he optimum. Figure 4.21 shows the displacement

magnitude contours for prototype 2. Note that the displaccment is non-syrnmetric with

respect to the mid-plane and that the maximum occurs again at the bouom bmcket.

•

L.Mrl sa: 1 - RIDIHC LOoUlS~ OF Ra: Ht:llERIALPLV S~ - v HIN:-l.1'~

~

•

Figure 4.20: Prototype 2 - Y-Normal Stress, Layer 1

Rlcllng loadsMaterla1!hlmeofreferenœDIsplaœment magnitude

Figure 4.21: Displacement Contours or Prototype 2

PLY HO: 1

::::::1::::1

32

1.9-1.3

D.6

DD

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65

Considering the large stress values as seen l'rom Figures 4.1 S. -L1lJ and 4.20.

rcinforcement was added to the ho[[om hrack<:t r<:gion of prololype 2. Two 45° wo"<:11

layers were added to the 6 iayer laminate already pr<:sent in this r<:gion. This allow<:d not

only the shear slresses to be r<:duced bUl also the x and y-normal stresses as weil. The

shear slress. in panicular. reduced hy up ID 35<;" in one of Ihe plies. One observation

howe"er is that the location of the maximum stress did not change. This conlirms that a

geometric redesign would be necessary in this area. A ho[[om bracket geometry like

prolotype 1 is much more slllrdy and hence the stresses there arc better distrihuted.

The addition of the lWO 450 layers aIso incrcased the o"er.lll stiffness tremendously as seen

by reductions in fmme del1ections. Table 4.6 shows the displacements al the botton'.

br.lckct before and alier the addition of the 450 reinforcement. The largc X-global

(horizontal) displacemcnt is due to the large chain force. and thc reinforccmcnt greatly

improvcs thc stiffness in this dircction. In thc Y-global (vcnical) direction thc dist'lacemcnt

is not particularly affected by the laminate change as thc vcttical displaccmcnt is mostly duc

to the ovcmIl llexing of the fmmc mthcr thcn a local cffcct. Thc bottom br.lckct torsiona]

stiffncss is much improved with the addition of thc reinforcemcnt as can be seen by thc

reduction ofthc Z-global (out-of-plane) direction displaccment.

Without With Improvement

reinforcement reinf;>rcement (%)(mm) (mm)

Xg1obol2.9 1.8 38

Yg1obol-2.2 -2.0 9.0

Zglobol 3.0 2.2 27

Table 4.6: Bollom Brdcket Displacements With and Without Reinforcement

From the above observations. il should bc evident that a carbon liber fmme should be built

with as many different Ianunates \Vhich correspond to the diftèrent stress region: as the

goal should be to have a structure \Vith a uniform stress level throughout. This is achieved

\Vith the improved laminate for prototype 2.

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66

~.2.4.3 Prototype 3

For pmllllype 3. the resuils of a ply-by-ply analysis were oblained as was perfonned for

prototype 1and 2. and maximum failure indices arc summarized in T:lble -1.7.

X tcnsion Xcomp. Ytcnsion Ycomp. XY shcar

Max.F.1. 0.160 0.060 0.770 0.22-1 0.IS7

?ly# 3 5&6 S S ~

Table -1.7 : M:lximum FailllJ'e Index for Eaeh Layer of Prototype 3

Figures 4.22. -1.23. and 4.24 show the maximum X-stress. Y-stress and XY-shear stress

contour plots for prolotype 3. respeetivcly. Prolotype 3 is designed with a [0,l90L

unidirectional composite layup in the low load are:lS :md built up to a lU laver IOJ90J01.. - - '\

layup in the higher load area.s. As this is unidireclional materiaI. it is expceted that the

limiling factor will De matrix tcnsion. This is what is obscl'\'cd l'rom Table -1.7. Aiso. thc

fact that it occurs in ply S could have hcen expccted a.s it is a 90° layer which is the farthest

from the core. hence thc layer subjected to the most mmrix tcnsion duc to bending of the

li·ame. Figure -1.22 shows the liber stress in ply 3. The magnitude of stresses is high but

again the strength of the libers is correspondingly high resulting in quite low l'ailure

indices. The light area.s on the frame shown in Figure -1.22 arc high tensile stress are:lS.

They correspond mostly to arca.s of the frùl11e having only 6 layers. These regions show

highcr stresscs as therc is less matcrialto take up thc load. Note thal along thc main beam.

the linc between thc two layups coincides with the difference in lhe two stress levels.

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67

Pl..~' NO: 3

Figure 4.22: Maximum X-stress for Prototype 3

Figure 4.23 shows the maximum Y-stress for prototype 3 in ply 8. ln Figure 4.23. the

light regions are regions where no or low stresses exist because in most of the frame there

is no ply 8. hence no stress to be displayed. The maximum matrix ten~ion stress is found

in the back of the seat bearn. Hence as this is the region where the highest failure mdex

exists on the frame. it is the first region where the frame should be reinforced. If we

follow the procedure of adding reinforcement to the regions of highest failure index and

remove material from regions of low index until a desired failure index value corresponding

to the factor of safety is achieved. the lightest frame for this factor of safety will be

obtained. Although this proposition is quite true for a given load and boundary condition

and quite acceptable in theory. in practice it is compJeteJy different. The Joad case changes

continually and hence no perfect theoritical layup will yieJd a unif."rm failure index

throughout. Even if the loading case was uniform in time. the manufacturing of such a

perfect Jayup with ail th' combination of layers and orientations would probably be

impossible. So. it is impossible to build a frame with a uniform failure index through(>ut.

•68

Figure 4.24 shows the XY-shear stresses throughout the frame with a maximum near the

bonom bracket. A1though this boltom bracket region is mueh more sturdy than for

prototype 2. it is expeeted that the maximum shear stresses will occur in this region.

In conclusiun. prototype 3 forms a very efficient structure from a finite-element analysis

point of view, but the manufacturing of such a frame by the construction method used

might be much more difficult because of the geometry with so many sharp corners. Time

constraints combined with this manufacturing problem prevented tbis frame from being

constructed as part of tbis project.

•

t.OAJl SET: 1 - EFFORTSQ.ASSIQUESFRSltIE OF REF: CLDBALPLY STRESS - y HIH:-1.O'SE+08 HAX: 6.3:E-.o7

Figure 4.23: Maximum Y-Stres~ for Prototype 3

PLY HO: 8

'.:rn:-.o7 _

~

::::1

•

•

l):ID SET: :. - ~Sa.t:.SSIQUES

F'Pl:lI1( OF' REF: Cl"OMl.PLv ~rm:~ - ~ HtN:-1.01C--oa lW<:

Figure 4.24: Maximum XY-Shear Stress for Prototype 3

69

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Chapter 5

Composite Frame Fabrication and Testing

5.1 Introduction

As previously discussed. the second pan of this project includes the construction of two

carbonlepoxy monocoque bicycle frames. Prototypes 1 and 2 wcre constructed. This

section will explain in detail the method. instruments. and matcrials uscd in the construction

of those frames. The final curing of prototypes 1 and 2 took place in Scptembcr 1994 and

June 1995 respectively. The methods used to test the frames will also be explained. The

test results for the composite frames will be compared to tests performed on c1assic metallic

frames.

5.2 Rationale for Manufacturing Method

The manufacturing method chosen is the thermoset prepreg-vacuum bagging method

outlined in section 2.5.4. It was chosen because as this study is still in the prototyping

stage, only one or two models of each frame was initially planned. Hence an expensive

aluminum or composite mold would not be appropriate. The thermoset prepreg material

was chosen over the wet lay-up and thermoplastic composite because it proyides good

mechanical properties, the correct fiber to resin volume fraction, an appropriatc tackiness

for fabrication and a relatively low cost compared to woven or unidirectional thermoplastic

prepregs. It is clear that fmal production of frames, large or small. should use an exterior

mold either with an internai bladder or an internai core, both for fabrication time reduction

and appropriate surface finish. For the reasons mentioned above, it was clear that the

thermoset prepreg-vacuum bagging technique was the best choice for this project.

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5.3 Fabrication of Prototype 1

Prototype 1 is the first carbon liber fr.lme huilt at McGili Universily. It is an experimental

fr.lme .md thus the whole fabrication process \Vas experimental. This prolotype \Vas

constructed for two main reasons. The tirst reason \Vas to experiment \Vith the

manufactUl;ng technique to see if it yielded acceptable resulls. The second reason \V.IS to

verify if the finite-e1ement analysis COl!ld c10sely model the actual situation. Keeping these

Iwo rea..~ons in mind. the fabrication should be \Vdl underslOod and appreciated. This t'rame

Wa..~ not meant for hard mcing. and possibly not even for casual riding. The following

sections explain in detai! the differcnt materials and procedures used in the production of

this prototype.

5.3.1 Foam

The core of the fmme is made of high performance rigid PVC foam. This was chosen in

order to provide a stable platform for shaping at a relatively low weight with appropriatt:

mechanieal properties. The properties of the Klegecell R75 foam arc shown in Table 5.1.

Density 75 kg/m'

Compressive Strength 1.29 MPa

TensileStrength I.Sl.'i MPa

Flexur:ù Strength 1.9S MPa.' . . .

. ShearStrength 1.04 MPa. .

. Elongation at break . 3.5%..... '.'

Table 5.1 : Meehanical Properties of the Foam Used for Prototype 1 [69]

Due to eomplicated and costly numerieal control machining. the foam was shaped using

manual labor techniques. A combination of hot-wire. band saw. exaeto knives and sand

paper was used to shape the 3 foam pieees. The linal foam shape wa..~ made from tmee

pieces glued together as the thiekness of the available foam wa..~ not suflicient for the

required thiekness of the rear part of tile model. The final foam shape weighted 901g.

Figure 5.1 shows the foam core with the a1uminum inscrts attached to il.

•

•

Figure 5.1 : Prototype 1 in the Curing lig

5.3.2 Foam Adhesive

In order to fabricate the foarn mode!. 3 picces of foarn had to be fastened togcthcr. Both

the left and right rear stays had to be fastened to the main body. The fa.lm pieces wcre

bonded together using Ciba-Geigy's fastweld epoxy adhesive [69]. This adhesive is fast

curing and appropriate for PVC foarns.

5.3.3 Inserts

Aluminum inserts were bonded to the foarn at different locations. Thc function of these

inserts is to allow the different components to be attached to the carbon fnune. These

metallic reinforcements were placed between the inner foarn core and the extcrior layer of

composite mr"erial. The main purpose of these inserts is to transfer :he loads through a

large bonding area from the composite material to the extemal agents. Aluminum inserts

were used at the bottom bracket, the rear dropouts. head tube and scat tube. Aluminum

was chosen for these parts because of its relatively low weight and ease of nuchining.

•

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Headset

The head~et was designed as a divergent channel w;th the top open. The exterior of the

fining was horizontally grooved to a depth of 1 mm to allow for a beller resistance to

vertically applied forces. The grooves a1low composite material to become embedded into

the insert during the curing process. The headset is shown in Figure 5.:2.

Figure 5.:2: Aluminum Headset

The inner diameter of the head tube was machined to fit a standard heads<,l. The headset

insert weight was l66g.

Bottom Bracket losert

The bottom bracket insert consists of 3 pieces. One tube houses the bonom bracket

cartridge. and is supported on both sides of the frame by a grooved a1uminum plates meant

to be embedded in the foam. The bonom bracket armngement is shown in Figure 5.3. The

bonom bracket inscrt weight was 7Ig.

Figure 5.3 : BOllom Bracket

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74

Rcar Dropouts

The rear dropouts consist of an open channel closed at one end by the rear axle mOUnl. The

4 picccs of cach rear dropout were wclded togethcr. The channel is also grooved and the

bollom is closed for the sume rea.~ons as those described for the headsel. Figure 5.4 shows

the rear dropout design. The weight of the left dropout was 166g while the right dropout

weighed l7lg (difference duc to welding).

,....1

'- ,;..-- ------

Figure 5.4 : Rear Dropouts

Scat Tube

A se:1t tube of 28.6 mm extemal diumeter and 26.7 mm internai diumeter was inserted to a

depth of 5 inches into the foum core. The weight of the seut tube Wa.~ 33g.

As the carbon fiber is electrically conductive, it is possible that galvanic corrosion may

occur at the carbon-aluminum interface. This corrosion produces an oxide that renders the

interface weak and less than optimum. Hence in order to minimize the corrosion, etching

of the aluminum is perforrned prior to the bonding with the carbon. This etching process

reduces the chances of galvanic corrosion [71].

5.3.4 Curing Jig

In order to install the inserts onto the foum core and also in order to support the frame

during the curing process. a special modular jig was dcsigned and constructed [72]. This

jig is constructed in such a way as to prevent excessive warping of thc frame during curing.

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75

If any of Ihe parts of the frame were to move out of alignment ùuring the curing proccss.

the hike woulù hecome unsymmelric anù ùcpenùing on Ihe ùegrcc of misalignment. Ihe

hike would possihly he uscless. This jig was conslructed out of sleel and aluminum hy

unùergr.tduate students at McGilllnj. Il was designcd 10 he versatile and to he comp;ll:hle

with diffcrent framc sizes. The frame is helù in the jig by four main attachment points: Ihe

pcdal shart. the front tuhe. Ihe l'car forks. and the scat tuhe. Figure 5.1 shows the foam

fr.tme in Ihe jig. reaùy la he eovereù with the carbon liher materia!. Also. the aluminum

inserts can be seen.

5.3.5 Foam-Aluminum Adhesive

After the foam as heen corrcctly shapeù. il is f;lsteneù \Vilh the alumioum inserts and

installed on Ihe jig. At this point. it is critieal to make sure th;lt the foam. inserts. ;IOÙ jig

arc in pcrfect alignment. The aluminum inserts were fastened ta the foam core using

ADCHEM high strength epoxy (5300A resin. 5300B hardener) [731. Sorne properties of

this epoxy system arc outlineù in T~le 5.2. The epoxy was ;ùloweù ta cure for 48 hallrs~ .

before the clamps were removed. Only 22g of adhesive was used to seellre the inserts in

place.

Boiling Point 260°C

Tensile Strength 62MPa

Tensile Modulus 2.3 GPa

Table 5.2: Propcrties of the ADCHEM High-Strength Epaxy [73J

5.3.6 Carbon Fiber Material

The materialused for the construction of this prototype was obtained l'rom The Advanced

Composite Group Inc. [61 J. Both woven and unidirectional continuous libers were used.

As a very ligbt and stiff structure is required. it is important to use high performance

cominuous libers r.tther than chopped libers or mats. The woven material is a 4X4 twill

weave which uses AKZO HTA carbon fibers [61 J. The 4X4 twill weave is referrcd by the

manufacturer as a CFSOO1 weave and is very drapable. that is it conforms weil to double­

curvatures. The matcrial is preimpregnated with LTM25 low tempcr.tture curing epoxy in a

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B-stage. The unidirectional material uses the same lihers and epoxy system as the \Voven

material. The mechanical properties of hoth the unidireetional malerial and woven m;llerial

can he found in Table 4.2. The epoxy .-:ystem is low tempcmture curing (56°C) in order 10

he compatible with the maximum temper.lturc the foam ean withstand (77°0. The cured

thickness of one layer is 0.28 mm for the \Voven material and 0.17 mm for the

unidirectional material.

5.3.7 Material Orientation

Section 4.2.2.1 gives a detailed account of the material orientations used for the

construction of prototype 1.

5.3.8 Vacuum Bagging

After the carbon liber preprcg had been carcful1y applied to the foam core. other materials

had to be applied to the carbon liber in order to prepare for curing. A layer of rclea.~e lilm

(non-porous Teflon) is applied dircctly on the carbon libers. This thin lilm is applied in

order to enable the relea.~ing of the vacuum bag l'rom the l;nished part after curing. Then a

brcather layer was applied everywhere. The breather material is quite thick and al10ws the

passage of air. This layer helps the vacuum to spread everywherc under the vacuum bag.

A vacuum bag was then made around the whole structure. The vacuum bag is sealed ail

arollnd with vacuum gum. Figure 5.5 shows prototype 1 inside ilS vacuum bag.

Figure 5.5 : Vacuum Bagging of Prototype 1

•77

A vacuum hose is installed and the vacuum dra\Vn. Some minor air gaps may then bc

stopped \Vith vacuum gum until an adequate vacuum is obtained. A vacuum pressure of the

order of 0.9 atm is achicved.

5.3.9 Curing

After an adequate vacuum is obtained. the fr.lme is ready for curing. The fmme \Vas cured

in a controlled temper.ltur:: oven with the prescribed temper.llure prolï1e shown in Figure

5.6. This curing cycle is the one suggested by the material manufacturer. The slope for

the periods of heating and cooling arc imponant as a shallow slope (112°C/min.) does not

thermally stress the material as much as a steep slope. After curing. the vacuum bag.

breather layer and release film arc removed 10 revcal a fully cured carbon monocoque

bicycle fmme.

60

roomtempo

o

/

1 13.5 14.5

Figure 5.6 : Curing Cycle

TIME(h)

•After curing, the surface of the composite frame showed sorne wrinkles. These wrinkles

arc inevitable and arc a result of the imperfect vacuum bag. Some of the wrinkles arc minor

and arc formed from a slight amount of excess resin, while others arc a direct wrinkling of

the fibers. The resin wrinkles can be sanded off without any loss of structura! integrity.

•ïS

The tiher wrinkks .:ould be grinded off. hUI weaken the <:llmposite frame. The lib.:r

wrinkles appeared e\'enly throughout the frame. This prolotype was not sanded nor

painled. :IS estheti.:s was not imp0l1am for this mode!. Aiso. no, sanding bd"ore stali.:

lesting allows the possihility of examining the dl\:<:l (lI' the wrinkles againsl the tinile­

e!ement mode\. which of .:ourse. does nol .:ontain any wrinkles.

5.3.10 Mass Propcrties of Protot)'pe 1

Tahk 5.3 shows how much each suhgroup .:ontrihuted 10 lhe tinal \wight of protolype 1.

Prototype 1 Weight (g)

Foam 901

A1unùnum lnserts 607

Glue and Filler 44

Composite 631

TotaI 21S3

Table 5.3: Summary ofWcighls lor Frc.lOlype 1

5.3.11 Conclusions and Recommended Improvements for

•

Prototype 1

As pn:viously specitied. this prototype \Vas constructed in :1l1 allempt to beeome familiar

with the fabrication method and to v:llidate the tinite-e!ement analysis of composite

structures of this type. The lirst and must substantial improvement which resulted l'rom the

fabrication of this prototype is the realization that the \wight of the aluminum inserts and

the 10am should be reduced. A wcight of 2183g for a composite frame is far too heavy.

Another fact rcalized is that a fl'".lme \Vidth of 75 mm waS too \Vide. A \Vide fmme is very

bad aerodynamically. This fmme seemed genel'".ùly too bulky. hence rcduction of the

fmme thickness \Vas in order. Prototype 2 \Vas built \Vith a nominal thickness of 50 mm.

This reduction in \Vidth by 33% helped reduce the volume and hence the \Veight of foam

used. Prototype 1 also had another basic problem. Il could not be used as a time trial

bicycle because therc is no possibility lor mounting the chain and rear del'".lilleur on the

•

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il)

insid.: of th.: r.:ar slays. No r.:ar d.:railkur can b.: instalkd. so lh.: war sprock.:t wou Il! h,m.:

10 b.: mounl.:d on th.: oulsid.: of lh.: r.:ar right stay. This is so b.:caus.: th.: 10p part of th.:

chain cannot pass l'rom th.: front chainring to th.: r.:ar sprock.:t without b.:ing in connict

with th.: fram.: ilS.:!!". As this lyp.: of fram.: can only hl: of limil.:d us.:. a fram.: d.:sign

allowing bath road tim.: trial with r':,lr d':l~lÎlkur and Irack racing capahility is mol'':

advantag.:ous. The only way ta modify this fram.: with its r.:ar stay g.:om.:try. to b.: us.:d

as a tilll': trial frame. would b.: 10 mak.: a hale in th.: fram.: al the location wh.:re the upp.:r

part of lhe ehain meets the frame. The bicycle used by :; time Tour de FraI/CC champion

Miguel Indurain in the time trials buill by Pinarello of haly incorporales this feature. An

oval holc is made on the right rear stay in order to allow the chain to go through. Figure

2.16 shows the Pinarello fmme with the access hole for the chain.

Another improvement to prototype 1 would be lhe reduction of lhe number of wrinkles

present on the frame. This wouId of course result l'rom the use of ,m eXlerior mold.

Alternativ.:!y. greater care in the fabrication of the vacuum bag \VouId allo\V a reduction in

the number of wrinkles. Another way to lower the numhl:r of wrinkks is ta make sure that

ail the carbon liber layers arc applied tighùy to each other. Loosely applied layers have a

greater tendency to wrinkle when compacted by the vacuum pressure.

In summary, the fabrication of prototype 1 was a success for what it \Vas intended to

provide. Il was the Iirst carbon liber monocoque fr.lme eyer built at ivIcGill. and it yielded

encour.lging results. It permilled the acquisition of a great deal of expcriencc and hands-on

realization of potenti.ll problems encountered in composite construction. Figure 5.7 shows

prototype 1 .IS it would look ready for riding (note without pedais or ·hain).

Figure 5.7 : Completc:d Prototype 1

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5.4 Fabrication of Prototype 2

The fabrication of prototype 2 was intended to yield a rideable. low weight monocoque

carbon liber frame. However. the prepreg-vacuum bag technique is still used and will

ultimately yield an imperfect surface finish. This frame could he used as a very deccnt time

trial vehicle. Also. it could be used as a marketing tool for future investors in order to

make an association between McGill University and interested bicycle manufacturers.

Having gained the experience from two monocoque carbon frames. it would he possible to

stan a smaii production of fmmes with the use of an exterior mold. but still using the same

shape. Hence the aim with this prototype is to make a lina! design which couId he rideable

and marketable.

5.4.1 Foam

Prototype 2 used a different foam than that used for prototype 1. This decision to change

the internai loam materiai for a lower density materiai was based on many reasons. The

first reason was to reduce the overall weight of the foam core. The internai core weight of

90!g for the first prototype was considerab!y high in order to produce a complete frJ.me

with a competitive weight. The foam used for prototype 2 was a very Iight PVC foam

manufactured by Divinycell [74]. ILS density 01 .lnly 45 kg/m' is 60% of the foam density

uscd for prototype 1. The second reason for a lower density foam material is an

improvement in the dynamic behavior of the frame. !t was shown that a lower density

internai core improves the dynamic properties by increasing the naturJ.! frequencies of the

fr.une [53]. The third reason for reducing the foam weight ani::-'lence reducing il~ materiai

properties is that the finite-element mode! does not consider the presence of an internai core

at ail. The foam core is there to separate the !eft and right shells of the fr.une. but does not

contribute to the structura! pr0p"rties. Based on those 3 reasons. it seems reasonab!e to

reduce the foarn density. Hence; any core present even with low mechanical properties

will improve the overai! integrity of the frame. The new foarn was aIso very easy to shape.

The overai! foarn core had to he macle out of 3 pieces as the thickness oi the foarn was not

enough for the required thickness al the rear stays of the frame. The 3 parts are

respective!y the main body. the left and the right rear stays.

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SI

5.4.2 Foam Adhesives

As for prototype 1. the 3 foam pieces \Vere fastened together using Ciba-Geigy's fastwcld

epoxy adhesi"e [70]. See section 5.3.2 for further adhesi"e properties.

5.4.3 Inserts

Aluminum inserts were again used in order to make the interface bctween the carbon skin

and the bicycle's extemal components. Inserts were machined for the rcar dropouts. the

headsct. the bottom br..lcket and the scat tube. The goal for prototype 2 was to rcduce the

ovemll wei"ht of the fmme. hence;m effort was made to rcùuce the wei"ht of all thee e

ins'~rts to a minimum. The total inserts weight on the tirst prototype \Vas 603g. A goal to

reduce the weight of the inserts by 50% was sel forward for this seeond prototype.

As a result of a study on carbon-aluminum-foanl intertàces made by undergr..lduate studenl~

[75] it was shown that the required load tr..lIlsfer surface l'rom the carbon skin to the

aluminum inserts was much smaller than expected. The design thus concentr..lted on

producing inserts that were very light. while still allowing for adequate bonding and

allachmcnt capabiliùes.

Headset

The headset of prototype 2 is made l'rom two sepamte pieces. The tirst piece is a

cylindrical section which will accommodate the headset ~ngs. The second part is a plate

which is bent around the cylinder and bonded to il. It is bonded to a recessed portion of the

cylinder in order to permit the 0.9 mm plate to be supported l'rom the bollom. The two

aluminum pieces were bonded together using Locùte 330 Depend no-mix adhesive [76].

This adhesive is suitable for structura! fastening as was required here. As the fastening

surface was quite large (approximately 2500 mm~). the bonding is quite adequate. The

total weight of the headset is 58g (30g for the plate and 28g for the cylinder). Figure 5.8

shows the head tube cylinder while Figure 5.9 shows the head tube plate.

•

31 dia. "

33 dIa.

I~30 dIa.

•,

'",~'Q, ,-,

•,,,,,,•••,,,,,,••,,

F,,,,

•

Figure 5.8: Head Tube Cylinder (all dimensions in mm)

1· "'----1I~_IF

Figure 5.9: Head Tube Plaie (all dimensions in mm)

Bottom Bracket

The bonom bracket is made of 3 pans. It contains the bonom bracket cylinder which gocs

through the frame and one plate recessed in the foum on both sides of the fr.une in order to

secure the cylinder in place. The bonom bracket cylinder is intemally threaded with a

1.370X24 Ieft handed thread at one extremity and a right handed thread at the other

(standard procedure). These threads were cut in order to mect with the bottom bracket

cartridge pedal case. Both bonom bracket plates recessed in the foum were_bonded to the

•-"ü."'I

t~,am using Ciha-Geigy's Fast\\'cld adhesi\"e liO] :md honded to the cylind~r lIsing the

Loctite 330 Depend adhesi\"e [i6]. Figure 5.10 shows the honom hrackel cylinder insen.

The \\'eight of the bonom bracket cylinder \\'as 49g \\'hile the t\\'o end plates \\'eighed lOg

each.

68

19 19

~I

38 dle

L.H. /Thread fram lert end1.370X24

R.HThreca from nght end1.370X24

•

Figure 5.10 : BOllOm Bracket Inser!

Rear Dropouts

One of the major improvements in the inscr! design was the rear dropouts. The design for

prototype 1 was made by welding 4 a1uminum pieces together. The result was a very

hcavy structure weighing on the order of 170g for cach dropout. The rear dropouts for

prototype 2 were made by machining one a1uminum piece with no welds. It resulted in a

much more compact design at a weight of 29g for cach dropout.

•

•

Scat Tube

A s~at tube with an ~xt~rnal diam~l~r of 28.6 mm diam~t~r anG an inl~rnal diam~t~r of 26.7

mm diam~t~r was ins~rt~d :;60 mm inlo Ih~ foam cor~. Th~ s~at tube was h()nd~d 1<' th~

foam corc using Ciha-G~igy's Fastwcld adh~si\'c 170J. Th~ wcight of th~ scal tubc was

Mg. Th~ s~al tuh~ inscr, is shown in Figur~ 5.11.

28.6 dl.J.

H-,--

389

!

26.9 dia.

Figure 5.1 1 : Seat Tube Insert (ail dimensions in mm)

5.4.4 Foam-Aluminum Adhesive

Similar 10 prototype I. after the inserts had been machined, they \Vere glued to the foam

core while the frame was in the curing jig. in order to make sure that the frame and the

inserts were in perfect aIignment. Before the inserts were gIued to the foam core, they

were thoroughly etched using West System's aIuminum etching kit [71]. This surface

treatment for aIuminum cIeans the surface and applies to it a protective coating which

•

•

prevents the oxidation at the aluminum-foam or aluminum-carhon interface. The adhesive

used \Vas the Fast\Vcld epoxy hy Ciha-Geigy [iO].

5.4.5 Internai Shifting Cable

A shifting cable \Vas embedded in the foam core hdore the application of the carbon liber

materiaJ. The pUI-pose of this cable is to aetivate the rear der.lilleur from the handlcbars.

An internaI routing method \Vas chosen for both aerojynamie and aesthetic reasons. It \Vas

hcld in place on the foam \Vith Ciba-Gcigy's Fas!wcld cpoxy adhcsive [iO].

5.4.6 Carbon Fiber Material

The materiaJ uscd for the construction of this prototype \Vas \Voven materiaJ obtaincd from

the Advanced Composite Group Inc. [611. It is the same as \Vas uscd for prototype 1.

However. no unidircctionaJ materiaJ was used on this fmme. The rcason for not using

unidircctionaJ materiaJ was discussed in section 4.2.2.2.

5.4.7 Material Orientation

The materiaJ orientation used for this prototype was consistent with the linite-elemem

model as mueh as possible. The exaet matehing of materiaJ orientation betwcen the finite­

clement model and the fiaished prototype is viltuaJly impossible. If proper patterns arc

preparcd before the lay-up is done. a better mateh between theory and pmetice ean be

aehieved. Refer to seetion 4.2.2.2 for the development of the laminate.

5.4.8 Vacuum Bagging

After the layers of earbon fiber were applied over the fmme. the other vaeuum bagging

materiaJs were applied on the frame. The release film and vaeuum bag were thus applied

and vacuum dmwn from under the bag. Before the introduction in the oven. the last air

leaks were removed to in order to assure a proper vacuum. A vacuum of 0.9 atm was

obtained under the vacuum bag. Figures 5.12. 5.13 and 5.14 show 3 stages of the layup

process

•

Figure 5.12 : Proto. 2 - Prepreg Application Figure 5.13: Proto 2.- Release Film

•

,-­Figure 5.14: Vacuum Bag Applied to the Frame

5.4.9 Curing

The curing cycle for prototype 2 \Vas exactly the saIlle as for prototype 1. hence refer to

section 5.3.9 and Figure 5.6 for further details.

•

•

SA.IO Final :\sscmbl~' of Protot~·pc 1

Pn't~'IYI'1: .:. \\~I;-' cnmrk~tdy assc.:l1lbkd \\,jlh sland~ll\l bi ..... y,,:k I..·\lmplltll.:nh. 'l) l'l\)fl!

dcraillcur nor n:ar hrakc.: was mULlr1tc.:d on t!l(' rnHlltypc.:. Th~' rc.:~I;--I)J1 fl)r Ih'i il1l."ludin.:= tilc.:;..l..~

fc.:~ltlln:s \\'as to kc.:c.:p thl.: dc.:sign and Il1~lIlll(a('tllrin~ ~IS .... imph: a;-. possihk. :\" thl..' frnnl

hrake is mounted direetly on the front fork. no pn1\j,il1l1 had to be made fllr hrakes lm th,'

l'raille. The utility of a front derailleur \\'as not eomplctdy neee"ary as the use of this

frame is still experimentaI. thus the S speeds pro\'ided hy the rear eng gears arc suflieient

for road testing. Tahle 5.4 gi\'cs an accollnt of the comron~nts whil.:h wcre mOllntcd on

prototype 2.

Front fock Columhus Foderi Lalllinati

Front brake "Ioclolo Sporting

Bottom bracket cassette Shimano BB U1':·5 1

Searpost Gipielllmc

Sear Gipicmmc

Pedal cranks GipiClllmc

Pedals Gipicl111IlC

Frontwheel Spccializcd 3·spokc composite-

Rearwheel Ma\'ie 3G-Front chainring . 52 tccth Gipicmmc

Rear derailleur: .. Shimano 600. '. . .,

cogs 8 spccd. 12-23 Shimano 600

Headset .' . , . Shimano 105

Handlebars Prolllc bars mountcd on norm.ll road

handlcbars

Ergolevers : Shimano 600 shiftlbr.lkc Ic\'crs

Table 5.4 : Componcnts

•

•

SA. 11 \lass Propcrtics nI' Prntot~pc ~

Prototype 2 Weight(gl

Foam .+02

A1uminum lnsens 255

Glue and Filler 62

Composite Matena! LJï2

Total 1691

T~olc 5.5 : SUlllm~ry of Weight, for Prototype :::

5.4.12 Impro\'ements and Conclusions for Protot~·pc .,

Prototype ::: w~, ~n imlllen,e impro"ement l'rom prototype 1. ln ~ddition to the o\.er.lll

,trueturc geometry whieh i, lllueh more eftieient :ll di,triouting the rider induccd lo~d,. the

o"erall de,ign ~nd f~orieation of thi, prototype i, "ery lllueh irnpro"ed. Prototype::: h:l'

hetter designed inserts whieh arc mueh smaller in size and thu, lighter. Abo. the internai

fo~m core i, thinner ~nd made l'rom a lighter material. .-\11 in ail. there were impro"ements

rcalized o"er prototype 1. It is dear that other impro"ements eould he made if other

prototypes were buill. The main feature which could he impro"ed upon is the surfacc

linish. The vacuum bagging method makes a r.lther question:lble surfüce tinish on pieccs

of irrcgular cross section . .-\lso. the use of exterior molds on :m internai bladder technique

would c1iminate the necd for a foam core. Howe"er. with the resources ~vailablc.

prototype 2 satislied its goal as heing a rideablc carbon liher monocoque fr.ll11e of

acceptable quality. Figure S.IS shows the linished prototype::: with ail the eomponents

attached. ready to be ridden.

•

•

Figure 5.15: Finished Prototype 2

5.5 Composite Frame Testing

It is essential tO test the produced fmmes in order to assess whether the tinal constructed

product is compaùble with the computer clabor.lled mode!. To do this. it is essential to

chose a meth,xl for measuring the similarity or differencc bctween the modcled and

constructed versions. It is c1car that it is impossible to statically test the constructed

prototypes under riding load condiùons as too many restraints and loads render this

solution impractical. Thus the same tests as those performed on the conventional fr.tmes

will be performed on the constructed monocoque carbon liber prototypes. A.iso. using the

same tests will a1low comparison between the composite and tubular metallic fr.rmes.

Hence 2 of the 3 tests describt.'d in section 3.3.4 will he performed on the two constructed

carbon liber prototypes.

5.5.1 Prototype 1 Test ResuUs

As menùoned earlier. prototype 1 was not constructed as being a ridcable mode!. It was

constructed in order to better understand the finite-element modeling and to familiarize

ourselves with the manufacturing aspects. After its construcùon. prototype 1 was tested in

the specially built tesùng jig shown in chapter 3. Test l and 2 were performed on this

•

•

pnHolypl.:. Tahle :'.6 shows the.: c.::xreril1lc.:n{~d n:~Lllt~ l)ht~lirH.:d (Ill" IhL' 1\\\.) diIIL'!\:nt h.· ... r...

l"."nmhinc.:d with the.: lïnitc-dellll.:nl n.:sults nht~lincd 1'1.)1' :hL' ~~lllll..· ll.lad and rL· ... {r~1l111 ,ch.

Prototype 1 Test 1 Test 2

1

(mm) (mm)

FEA 2.70 1"+. :6

Experirnent:ll 2.50 1..1,:'

Difference % S.O I.S.

Tange Prestige (Steel) 0.53 1S.n

Trek 1100 (AI.) 1.1 .. 3... 1

Tahle 5.6: FEA :md Experimcntal RcsullS for Prototype 1

From thesc results. ohscr\"c that thc linitc...·1clllcnt results agrcc surprisingly wcll \\'ilh thc

cxperimcntal rcsults. This gi\"cs contidencc in furthcr tinitc-c1c'nent simulation and

eontidencc that the ehosen lay-up for further prototypes under the riding case would he

appropriate. The error margins for the compositc frJ.mes arc e\"en smaller than for the

comparison hetween the experimental and linite-c1ement results for the tuhular frJ.mes

shown in Tahle 3.2. This might arise from the fuel that shell clements arc much hetler

suited to nat skin structures like the composile frJ.mes. rJ.ther than curved surfaccs as those

used for modcling trJ.ditional frJ.nle tubes. The most important obser,ations from this

Table arc the \"alues obtained for both test 1 and 2 for prototype 1 comparcd tO the hest

aluminum and stec! fmmes tested. Prototype 1 is 28,/" stifter in the out-ol~plane direction

(test 2) than the Rocky Mountain fmme :lIld 4.7 times more compliant in the in-plane

direction as shown by test 1. From these results. we can obser\"e that some of the initial

goals were obtained. Prototype 1 is made from an internaI foam core 75 mm thick. This

large thickness assures rigidity in the out of plane direction. Hence. for this particular

prototype. bccause of ils thickness. the design shifts from bcing stiffness-based to bcing

strength-based as the eX!rJ. internal core thickness allows for an increased out-of-plane

rigidity.

•

•

5.5.2 Prototype ., Test ResuIts

..\s fnr pnltnlyp~ 1. prnl')lyp~: \\'as ~xp~rilll~'1tally I·:,t~d. Tahk ~.7 ,Ihl\\" Ih~ r~'lIlb nI'

l~'l 1 and : p~rfnrlll~d hnlh lIsinl; Ih~ FE.-\ appr"adl and ~xl'~rilll~nt;li!y. Th~ Tank alsn

indlllks_ f,'r ~nmparisnn 1'1Irpns~s. Ih~ r~slliis fnr pl\ll,ltyp~ 1. Ih~ n~sl sl~d fr;lll1~ ;md Ih~

;llul11inlllll fralll~.

Prototype 2 Test 1 Test 2

(mm) (mm)

Prototype 2-FEA 2.69 1... 36

Prototype 2- Exp. 2.5.. 13.ï3

Difference (%) 5.9 ... 6

Steel-Tange Prestige .53 1~.6

Aluminum-Trek. 1100 1.1 .. 3... 1

Prototype 1- Exp. 2.5 1...5

Tablc: 5.7 : FEA and Experim~ntal R~sults fôr Prototype 2

Note al;ain that the experimental and FEA results agree quite \\'dl. As a result of the

experil11entation \\'ith prototype 1. and the factthat the same eare \Vas taken for th~ study of

prototype 2. it is not surprising that close results \Vere obtained bet\Veen the experimental

and FEA study. Prototype:2 shows an out-ol'-plane rigidity 5.6'1" better than prototype 1

even though prototype 2 is 33% thinner and has an ovemll weight almost SOOg less than

prototype 1. Also. it shows an in-plane resiliencc very sil11ilar ta prototype 1. The most

important aspect ta rcmember l'rom this Tablc:. which is basically a summary of this

research. is that it is possible ta design a monocoque composite fr.une using FEA which

corresponds closely to the fabricated prototype. ln addition. this constructed thune cano at

a 10\Ver weight. exhibit more desir.lble features than the conventional tr.lditional tubular

frames.

•

•

5.6Summary

Th.: tirst pan of this chapt.:r has shown th.: proc.:Jur.: for rh.: construction of rh.: two

carbon lib.:r monocoqu.: fram.:s. Altho...gh th.: fabrication proc.:Jur.: chos.:n CllulJ only

apply to th.: construction of prototyp.:s. it has show;) 10 h.: v.:ry appropriat.: for this

purpos.:. Th.: w.:ight and surfac.: tinish of both prototyp.:s coulJ b.: improv.:J with th.: us.:

of anoth.:r production m.:thod. Lising another production m.:thod. such as an int.:mal

bladder technique. couid rcdu:.: th.: w.:ight of th.: frJ.m.:s to th.: rJ.ng.: of th.: lightest on th.:

mark.:t (1.2kg) while stil! showing .:xcdI.:nt stiffn.:ss attribut.:s comparcd to oth.:r light

frJ.mes which arc usually .:xtrcmcly tlexible.

Th.: s.:cond pan of chapter 5 was concemed with the testing of th.: fabricated frames and

comparison with metallic tubular frJ.mes tested under the same conditions using the sanle

apparatus. The rcsults have shown the composite frJ.mes to he stifter in the out-of-plane

direction and more resilient in the in-plane din.'Cùon. two attributes which arc beneficial for

a bicycle frame. It is thus encouraging to observe that the iniùal goal set forth has bt:en

met: to produce a carbon fiher monocoque frJ.me with dircctional!y tailorcd properties.

•

•

Chapter 6

Conclusion

The methodology for designing composite bicycle fr.lmes illustmtcs the importance of

using tinite-clement analysis as a way of minimizing the cost and time required for different

designs. The analysis can be effective for determining both geometry and tanùnale design

to oblain bener strength and stiffness char.lcleristics lhan tmditional tubutar franles. The

thrce carbon tiber monocoque fr.lffie designs presented are a resutt oi this design process.

From lhese designs. il is evident that a carbon tiber fr.ll11e shoutd be buitt using many

differenl laminates which correspond to the different stress regions as the goat shoutd be to

have a structure with a uniform stress tevelthroughout. The addition of local reinforcement

has been shown to reduce local stresses. Local reinforcement can be added to the fr.lffie

with a minimum increase in overJ1l \wight.

Finite-element analysis wa.~ also used to numerically compute fr.lffie stiffnesses in order to

compare with experimental resull~ performed on tubular and composite ti-.lmes. Fr.lffie

stiffness is important when atlempting to design the fr.lffie for performance and rider

comfort. When discussing the stiffness of fr.lffies, it is actualty the directional stiffness that

the designer should he concemed \Vith as torsional stiffness is desir.lble white in-plane

stiffness is not. While frame stiffness is inherently involved in the process, it is the

intemction of the biomechanical characreristics of the individual rider with the bicycle that

ultirnately determines whemer me bicycle has a feel mat is too "sofe or too "stiff'.

Detennination of how me quantifiable fr.lffie stiffness characteristics relate to me qualitative

description of what me rider senses is an important factor to consider funher. It has been

successfuIly shown mat wim simple tests, different important franle stiffnesses can he

measured and can he used to quantify me quality of different fr.lffies.

•

•

The rrdin1il1~u'Y static tl.:stlI1:; t)f [r~lliitll)Jlal fr~lIl1l'''' \\ ~l' ~·"""'l·t1tial Il' t!ll'" r~"'l'~lI\,:h ~t ... H

p~rmill~Ù th~ ù~\dopm~nt ol'Ih~ I~slin~ !11~lho,b \\ hich \\ "llid he' lls~d f<'r lh~ c"rhon lihe:r

prolotyp~s holh ~xrc:rilll~nt"lIy and l1l111l~ri~ally. Th~ traJillon,d fralll~' pr<,dllc~J r~'1I1"

whkh w~r~ f<'lInJ {(l he invalll"hk for ~"mp"rison wilh Ih~ C<'!l'lru~I~J carhon lih~r

protolyp~s. "h a r~sllii ,,l' Ihis I~stin~. il wa, ,hown Ih"l th~ ,"ll1,lrllCI~d carhon nhe:r

rram~s sho\\~d slifrn~" "llrihlll~s whidl \\~r~ ck"rly 'lIp~rior 10 Ih~ he:sl tradilional fr:lIll~'

~xamin~d, It is illlport"nt l" not~ Ih,'1 Ih" illlrrll\~m~l1l \\,,, pr~dict~d \\'jlh Ih~ fll1jl~­

dClncnt ana.!ysis l..:'\"cn hcfon: the- tirst L'arhl..Hl lïlx-r framl~ W~l;-. l'\..l(1"tnll.:tl:d.

Th~ ,~cond pan or this r~s~","~h \\"S th~ J~\dOplll~nl of " mal1l1l'''~tllrin~ l~chniqll~ for

~omposit~ mat~ria! hicyde frames, The melhoJ ~hosen provideJ. al 10\\ ~osts. lh~ most

llexihk means of prodll~ingprototypes, The hanJ laynp of prepreg ~arh,)n1epoxy materia!

to an internaI roam eore \\as iJeal l'or pmtotyrc: moJding, The main inconwniences ",hich

resulted l'rom this method arc the linal sllrrac~ linish. \\hich is de","ly inappropriate l'or a

m","ketahlc produel. and the impossihility or removing the Internai core alkr curing, ln a

prodllction situation. it \\ould he: ess<:mia! to remove Ihe interna! core sincc in the

prototypes il contributes 25 to 40,;' or the timshed rr.une \\eighl. Prototype 1 achi~wJ its

goal or ocing a tria! prototype l'or th~ linit~-clcm~nt m~thod. rabrication method and to

devclop the testing procedures. Prototype 2 also matched its goal or being a rideable and

adequate pre-production prototype.

ln addition to ils high strength and stirrness propenies. it is the versatility or carbon liber

which makes it an excellent materia! l'or lightweight structures, Bicyde rr.lmes arc an

excellent exanlple or successrul application ûr this material.

•

•

95

Chapter 7

Recommended Further Research

As future and complementary research. several other aspects of composite bicycle design

should he exarnined in order to obtain a complete slUdy. With respect to the finite-element

modeling. it would he interesùng to model the frame using solid elemenL~ for the internai

core. A more detailed analysis could be perforrned on the metal/composite interfaces at the

joint locations. This could include considerJùon of titanium as a more compatible material

for use as insens. Also. in addition to the use of reinforcement. geometric redesign of

cenain regions should he considered in order to reduce the stresses to a minimum. Both

finite-element and experimental dynarnic loading should he perforrned in order to assure the

structural integrity. for example. due to high rate impact. Experimental fatigue testing

should he perforrned on the frames in order to assure long terrn structural integrity even

though carbon fiher is known to have excellent fatigue resistance. The complete series of

standards bicycle tests should he imposed on the prototypes in order to assure that the

production models would respect those standards.

This study was focused on the bicycle frame structural design. but aerodynarnie testing

should he perforrned in order to reduee the frame drag. Minute changes to structural cross­

sections may produce a huge reduction in aerodynarnic drag.

•

•

96

Further research and work on the fabrication method ta he used should be performed.

Bath the fabrication method of the prototypes and the fabrication method for large scale

production should be further examined. An appropriate. la\\' cast moulding procedure

should be devised.

Last but not least. therc is a potential for further rcsearch in non-conventionnai composite

fr.lme building materials. It seems that a thermoplastic matrix combined with new libers

such as Vectr.ln or Dynema could potentially rcvolutionize fr.ulle building. both in tl:e

quality of the products and in the marketing appeal which would emanate l'rom the use of

these new materials.

Different geometries and loading cases could also he e1abor.lted for differcnt types of uses

such as mountain biking. triathlon. olympic pursuit and even touring.

Analysis of the complete f=e as part of a complete dynamic system comprising of aIl

other components such as the front fork and wheels. A study of this type would l'ully

chamcterize the response of a f=e in a realistic situation with the intemction of all the

componenL~ .

•97

Publications Resulting from this Work

A) Patrick L. Lizone. Larry B. Lessard. James A. Nemes. "Design of Ad\'anced

Bicycle Frames". ATMAM 1994. Montreal. August 10-12 1994. pp. 90-97.

•

B) Larry B. Lessard. James A.Nemes. Patrick L.Lizone. "Utilization of FEA in the

Design of Composite Bicycle Frames", Composites, Vol 26, Number 1. pp Î2-

74, 1995.

C) Patrick L. Lizone, Larry B. Lessard, James A. Nemes, "Stress and Failurc

Ana1ysis ofComposite Bicycle Frames",\CCM-10, Whistler s.e., August \4-18

1995, Vol.lII, pages 70 \-708 .

•

•

9S

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17· Gould, R., "The Bike Built to Win", New Scienrisr. June 30 1990. pp. 49-5 I.

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99

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